Currently, you can't limit the fields because you can't be sure that all necessary fields are in a number of allowed.

You haven't mentioned if you use custom index or a default sitecore index (like "sitecore-web-index").

Anyway, in case you have a lot of fields and the amount of data in those fields, the best approach the tune a perfomance is to create your oun index with custom configuration. 

Then, in the custom configuration, set `false` value for the `indexAllFields` property:

    <indexAllFields>false</indexAllFields>

The next step is to include just necessery fileds. For example:

    <include hint="list:AddIncludedField">
        <fieldId>{8CDC337E-A112-42FB-BBB4-4143751E123F}</fieldId>
    </include>

Also you can set included/excluded templates that should be included/excluded in index (more precisely, items that are based on them):

    <exclude hint="list:AddExcludedTemplate">
        <BucketFolderTemplateId>{ADB6CA4F-03EF-4F47-B9AC-9CE2BA53FF97}</BucketFolderTemplateId>
        <!-- And etc -->
    </exclude>

    <include hint="list:AddIncludedTemplate">
         <ContentPage>{04AA33EA-4677-488F-A39A-BDDAE504250E}</ContentPage>
         <HomePage>{23FE027D-1375-4D8C-A2FB-B70276F43C71}</HomePage>
         <!-- And etc -->          
    </include>

Also you can define a root path for crowler which will also limit a number of items in the index:

    <locations hint="list:AddCrawler">
        <crawler type="Sitecore.ContentSearch.SitecoreItemCrawler, Sitecore.ContentSearch">
             <Database>web</Database>
             <Root>/sitecore/content/Websites</Root>
        </crawler>
    </locations>

Adding the custom index will definitelly positively affect an index size and number of fields in the index.

Example of custom search configuration:

    <configuration xmlns:patch="http://www.sitecore.net/xmlconfig/">
      <sitecore>
        <contentSearch>
          <!-- Configuration sections for indexes -->
          <indexConfigurations>
    
            <!-- If an index has no configuration specified, it will use the configuration below. The configuration is not merged if the index also has
                 configuration, it is either this configuration or the index configuration. -->
            <CustomSearchIndexConfiguration type="Sitecore.ContentSearch.SolrProvider.SolrIndexConfiguration, Sitecore.ContentSearch.SolrProvider">
              <!-- This flag will index all fields by default. This allows new fields in your templates to automatically be included into the index.
                   You have two choices : 
                   
                   1) Set this to true and place all the fields you would like to remove in the 'ExcludeField' list below.
                   2) Set to false and place all fields you would like to be indexed in the 'IncludeField' list below.
                -->
              <indexAllFields>false</indexAllFields>
    
              <!-- Should index Initialize() method be called as soon as the index is added or wait for an external trigger -->
              <!-- For Solr Initialize() needs to be called after the IOC container has fired up -->
              <initializeOnAdd>false</initializeOnAdd>
    
              <!-- DEFAULT FIELD MAPPING 
                   This field map allows you to take full control over how your data is stored in the index. This can affect the way data is queried, performance of searching and how data is retrieved and casted to a proper type in the API. 
                -->
              <fieldMap type="Sitecore.ContentSearch.SolrProvider.SolrFieldMap, Sitecore.ContentSearch.SolrProvider">
                <!-- This element must be first -->
                <typeMatches hint="raw:AddTypeMatch">
                  <typeMatch typeName="guidCollection"     type="System.Collections.Generic.List`1[System.Guid]"     fieldNameFormat="{0}_sm"  multiValued="true"                    settingType="Sitecore.ContentSearch.SolrProvider.SolrSearchFieldConfiguration, Sitecore.ContentSearch.SolrProvider" />
                  <typeMatch typeName="stringCollection"   type="System.Collections.Generic.List`1[System.String]"   fieldNameFormat="{0}_sm"  multiValued="true"                    settingType="Sitecore.ContentSearch.SolrProvider.SolrSearchFieldConfiguration, Sitecore.ContentSearch.SolrProvider" />
                  <typeMatch typeName="intCollection"      type="System.Collections.Generic.List`1[System.Int32]"    fieldNameFormat="{0}_im"  multiValued="true"                    settingType="Sitecore.ContentSearch.SolrProvider.SolrSearchFieldConfiguration, Sitecore.ContentSearch.SolrProvider" />
                  <typeMatch typeName="guid"               type="System.Guid"                                        fieldNameFormat="{0}_s"                                         settingType="Sitecore.ContentSearch.SolrProvider.SolrSearchFieldConfiguration, Sitecore.ContentSearch.SolrProvider" />
                  <typeMatch typeName="id"                 type="Sitecore.Data.ID, Sitecore.Kernel"                  fieldNameFormat="{0}_s"                                         settingType="Sitecore.ContentSearch.SolrProvider.SolrSearchFieldConfiguration, Sitecore.ContentSearch.SolrProvider" />
                  <typeMatch typeName="shortid"            type="Sitecore.Data.ShortID, Sitecore.Kernel"             fieldNameFormat="{0}_s"                                         settingType="Sitecore.ContentSearch.SolrProvider.SolrSearchFieldConfiguration, Sitecore.ContentSearch.SolrProvider" />
                  <typeMatch typeName="text"               type="System.String"                                      fieldNameFormat="{0}_t"   cultureFormat="_{1}"                  settingType="Sitecore.ContentSearch.SolrProvider.SolrSearchFieldConfiguration, Sitecore.ContentSearch.SolrProvider" />
                  <typeMatch typeName="string"             type="System.String"                                      fieldNameFormat="{0}_s"                                         settingType="Sitecore.ContentSearch.SolrProvider.SolrSearchFieldConfiguration, Sitecore.ContentSearch.SolrProvider" />
                  <typeMatch typeName="int"                type="System.Int32"                                       fieldNameFormat="{0}_tl"                                        settingType="Sitecore.ContentSearch.SolrProvider.SolrSearchFieldConfiguration, Sitecore.ContentSearch.SolrProvider" />
                  <typeMatch typeName="bool"               type="System.Boolean"                                     fieldNameFormat="{0}_b"                                         settingType="Sitecore.ContentSearch.SolrProvider.SolrSearchFieldConfiguration, Sitecore.ContentSearch.SolrProvider" />
                  <typeMatch typeName="datetime"           type="System.DateTime"                                    fieldNameFormat="{0}_tdt" format="yyyy-MM-dd'T'HH:mm:ss.FFF'Z'" settingType="Sitecore.ContentSearch.SolrProvider.SolrSearchFieldConfiguration, Sitecore.ContentSearch.SolrProvider" />
                  <typeMatch typeName="long"               type="System.Int64"                                       fieldNameFormat="{0}_tl"                                        settingType="Sitecore.ContentSearch.SolrProvider.SolrSearchFieldConfiguration, Sitecore.ContentSearch.SolrProvider" />
                  <typeMatch typeName="float"              type="System.Single"                                      fieldNameFormat="{0}_tf"                                        settingType="Sitecore.ContentSearch.SolrProvider.SolrSearchFieldConfiguration, Sitecore.ContentSearch.SolrProvider" />
                  <typeMatch typeName="double"             type="System.Double"                                      fieldNameFormat="{0}_td"                                        settingType="Sitecore.ContentSearch.SolrProvider.SolrSearchFieldConfiguration, Sitecore.ContentSearch.SolrProvider" />
                  <typeMatch typeName="stringArray"        type="System.String[]"                                    fieldNameFormat="{0}_sm"  multiValued="true"                    settingType="Sitecore.ContentSearch.SolrProvider.SolrSearchFieldConfiguration, Sitecore.ContentSearch.SolrProvider" />
                  <typeMatch typeName="intArray"           type="System.Int32[]"                                     fieldNameFormat="{0}_im"  multiValued="true"                    settingType="Sitecore.ContentSearch.SolrProvider.SolrSearchFieldConfiguration, Sitecore.ContentSearch.SolrProvider" />
                  <typeMatch typeName="datetimeArray"      type="System.DateTime[]"                                  fieldNameFormat="{0}_dtm" multiValued="true"                    settingType="Sitecore.ContentSearch.SolrProvider.SolrSearchFieldConfiguration, Sitecore.ContentSearch.SolrProvider" />
                  <typeMatch typeName="datetimeCollection" type="System.Collections.Generic.List`1[System.DateTime]" fieldNameFormat="{0}_dtm" multiValued="true"                    settingType="Sitecore.ContentSearch.SolrProvider.SolrSearchFieldConfiguration, Sitecore.ContentSearch.SolrProvider" />
                </typeMatches>
    
                <!-- This allows you to map a field name in Sitecore to the index and store it in the appropriate way -->
                <!-- Add schema fields here to enable multi-language processing -->
                <fieldNames hint="raw:AddFieldByFieldName">
                  <field fieldName="__created_by"         returnType="string" />
                  <field fieldName="__smallcreateddate"   returnType="datetime" format="yyyy-MM-dd'T'HH:mm:ss'Z'" />
                  <field fieldName="__smallupdateddate"   returnType="datetime" format="yyyy-MM-dd'T'HH:mm:ss'Z'" />
                  <field fieldName="__workflow_state"     returnType="string" />
                  <field fieldName="extension"            returnType="text" />
                  <field fieldName="title"                returnType="text" />
                </fieldNames>
    
                <!-- FIELD TYPE MAPPING
                     This allows you to map a field type in Sitecore to a type in the index.
                     USAGE: When you add new field types to Sitecore, add the mappings here so they work through the Linq Layer 
                  -->
                <fieldTypes hint="raw:AddFieldByFieldTypeName">
                  <fieldType fieldTypeName="checkbox"                                                                                                 returnType="bool"             />
                  <fieldType fieldTypeName="date|datetime"                                                                                            returnType="datetime"         />
                  <fieldType fieldTypeName="html|rich text|single-line text|multi-line text|text|memo|image|reference"                                returnType="text"             />
                  <fieldType fieldTypeName="word document"                                                                                            returnType="text"             />
                  <fieldType fieldTypeName="integer"                                                                                                  returnType="long"             />
                  <fieldType fieldTypeName="number"                                                                                                   returnType="float"            />
                  <fieldType fieldTypeName="icon|droplist|grouped droplist"                                                                           returnType="string"           />
                  <fieldType fieldTypeName="checklist|multilist|treelist|tree list|treelistex|tree list|multilist with search|treelist with search"   returnType="stringCollection" />
                  <fieldType fieldTypeName="name lookup value list|name value list"                                                                   returnType="stringCollection" />
                  <fieldType fieldTypeName="droplink|droptree|grouped droplink|tree"                                                                  returnType="stringCollection" />
                </fieldTypes>
              </fieldMap>
    
              <documentOptions type="Sitecore.ContentSearch.SolrProvider.SolrDocumentBuilderOptions, Sitecore.ContentSearch.SolrProvider">
                <!-- GLOBALLY EXCLUDE TEMPLATES FROM BEING INDEXED
                   This setting allows you to exclude items that are based on specific templates from the index.
                -->
                <exclude hint="list:AddExcludedTemplate">
                  <BucketFolderTemplateId>{ADB6CA4F-03EF-4F47-B9AC-9CE2BA53FF97}</BucketFolderTemplateId>
                </exclude>
    
                <!-- GLOBALLY INCLUDE TEMPLATES IN INDEX
                   This setting allows you to only include items that are based on specific templates in the index. You must specify all the
                   templates that you want to include, because template inheritance is not checked. 
                   When you enable this setting, all the items that are based on other templates are excluded, regardless of whether the template
                   is specified in the ExcludeTemplate list or not.
                -->
                 <include hint="list:AddIncludedTemplate">
                   <ContentPage>{04AA33EA-4677-488F-A39A-BDDAE504250E}</ContentPage>
                   <HomePage>{23FE027D-1375-4D8C-A2FB-B70276F43C71}</HomePage>
                   <NewsPage>{582D070C-D82F-4DC7-8B6F-C3E12FA36F3E}</NewsPage>
                </include>
    
                <!-- GLOBALLY INCLUDE FIELDS IN INDEX
                   This setting allows you to specify which fields to include in the index when the indexAllFields setting is set to false.
                -->
                <!--<include hint="list:AddIncludedField">
                <fieldId>{8CDC337E-A112-42FB-BBB4-4143751E123F}</fieldId>
                </include>-->
    
                <!-- GLOBALLY EXCLUDE FIELDS FROM BEING INDEXED
                   This setting allows you to exclude fields from the index when the indexAllFields setting is set to true.
                -->
                <!--<exclude hint="list:AddExcludedField">
                  <__Created>{25BED78C-4957-4165-998A-CA1B52F67497}</__Created>
                </exclude>-->
    
                <!-- REMOVE INBUILT SITECORE FIELDS
                   This allows you to store a field in different ways in the index. You may want to store a field as Analyzed and Not Analyze
                -->
                <fields hint="raw:AddExcludedSpecialField">
                  <remove type="both">AllTemplates</remove>
                  <remove type="both">Created</remove>
                  <remove type="both">Editor</remove>
                  <remove type="both">Hidden</remove>
                  <remove type="both">Icon</remove>
                  <remove type="both">Links</remove>
                  <remove type="both">Updated</remove>
                </fields>
    
                <!-- COMPUTED INDEX FIELDS 
                   This setting allows you to add fields to the index that contain values that are computed for the item that is being indexed.
                   You can specify the storageType and indextype for each computed index field in the <fieldMap><fieldNames> section.
                -->
                <fields hint="raw:AddComputedIndexField">
                  <field fieldName="__smallcreateddate"             returnType="string"          >Sitecore.ContentSearch.ComputedFields.CreatedDate,Sitecore.ContentSearch</field>
                  <field fieldName="__smallupdateddate"             returnType="string"          >Sitecore.ContentSearch.ComputedFields.UpdatedDate,Sitecore.ContentSearch</field>
                  <field fieldName="_content"                       returnType="string"     type="Sitecore.ContentSearch.ComputedFields.MediaItemContentExtractor,Sitecore.ContentSearch">
                    <mediaIndexing ref="contentSearch/indexConfigurations/defaultSolrIndexConfiguration/mediaIndexing"/>
                  </field>
                </fields>
              </documentOptions>
    
              <mediaIndexing ref="contentSearch/indexConfigurations/defaultSolrIndexConfiguration/mediaIndexing" />
              
              <!-- VIRTUAL FIELDS
                   Virtual fields can be used to translate a field query into a different query.
                -->
              <virtualFields type="Sitecore.ContentSearch.VirtualFieldProcessorMap, Sitecore.ContentSearch">
                <processors hint="raw:AddFromConfiguration">
                  <add fieldName="daterange" type="Sitecore.ContentSearch.VirtualFields.DateRangeFieldProcessor, Sitecore.ContentSearch" />
                  <add fieldName="_lastestversion" type="Sitecore.ContentSearch.VirtualFields.LatestVersionFieldProcessor, Sitecore.ContentSearch" />
                  <add fieldName="updateddaterange" type="Sitecore.ContentSearch.VirtualFields.UpdatedDateRangeFieldProcessor, Sitecore.ContentSearch" />
                  <add fieldName="_url" type="Sitecore.ContentSearch.VirtualFields.UniqueIdFieldProcessor, Sitecore.ContentSearch" />
                  <add fieldName="_fullpath" type="Sitecore.ContentSearch.VirtualFields.FullPathFieldProcessor, Sitecore.ContentSearch" />
                  <add fieldName="parsedcreatedby_s" type="Sitecore.ContentSearch.VirtualFields.CreatedByFieldProcessor, Sitecore.ContentSearch" />
                </processors>
              </virtualFields>
    
              <!-- SITECORE FIELDTYPE MAP
                   This maps a field type by name to a Strongly Typed Implementation of the field type e.g. html maps to HTMLField
                -->
              <fieldReaders ref="contentSearch/indexConfigurations/defaultSolrIndexConfiguration/fieldReaders" />
    
              <!-- INDEX FIELD STORAGE MAPPER 
                   Maintains a collection of all the possible Convertors for the provider.
                -->
              <indexFieldStorageValueFormatter ref="contentSearch/indexConfigurations/defaultSolrIndexConfiguration/indexFieldStorageValueFormatter" />
    
              <!-- INDEX PROPERTY TO DOCUMENT MAPPER
                   Maintains a collection of all the possible Convertors for the provider.
                -->
              <indexDocumentPropertyMapper ref="contentSearch/indexConfigurations/defaultSolrIndexConfiguration/indexDocumentPropertyMapper" />
               
    
              <!-- DOCUMENT BUILDER
                   Allows you to override the document builder. The document builder class processes all the fields in the Sitecore items and prepares
                   the data for storage in the index.
                   You can override the document builder to modify how the data is prepared, and to apply any additional logic that you may require.
              -->
              <documentBuilderType ref="contentSearch/indexConfigurations/defaultSolrIndexConfiguration/documentBuilderType" />
    
              <defaultSearchSecurityOption ref="contentSearch/indexConfigurations/defaultSearchSecurityOption" />
    
            </CustomSearchIndexConfiguration>
          </indexConfigurations>
        </contentSearch>
      </sitecore>
    </configuration>

Example of custom index which uses the newly created configuration:

    <?xml version="1.0" encoding="utf-8" ?>
    <configuration xmlns:patch="http://www.sitecore.net/xmlconfig/">
      <sitecore>
        <contentSearch>
          <configuration type="Sitecore.ContentSearch.ContentSearchConfiguration, Sitecore.ContentSearch">
            <indexes hint="list:AddIndex">
              <index id="custom_sitesearch_index" type="Sitecore.ContentSearch.SolrProvider.SwitchOnRebuildSolrSearchIndex, Sitecore.ContentSearch.SolrProvider">
                <param desc="name">$(id)</param>
                <param desc="core">$(id)</param>
                <param desc="rebuildcore">$(id)_second</param>
                <param desc="propertyStore" ref="contentSearch/indexConfigurations/databasePropertyStore" param1="$(id)" />
                <configuration ref="contentSearch/indexConfigurations/CustomSearchIndexConfiguration" />
                <strategies hint="list:AddStrategy">
                  <strategy ref="contentSearch/indexConfigurations/indexUpdateStrategies/onPublishEndAsync" />
                </strategies>
                <locations hint="list:AddCrawler">
                  <crawler type="Sitecore.ContentSearch.SitecoreItemCrawler, Sitecore.ContentSearch">
                    <Database>web</Database>
                    <Root>/sitecore/content/Websites</Root>
                  </crawler>
                </locations>
                <enableItemLanguageFallback>true</enableItemLanguageFallback>
                <enableFieldLanguageFallback>true</enableFieldLanguageFallback>
              </index>
            </indexes>
          </configuration>
        </contentSearch>
      </sitecore>
    </configuration>