diff --git a/src/librustdoc/clean/types.rs b/src/librustdoc/clean/types.rs
index d34c2dba0b0d..026336982736 100644
--- a/src/librustdoc/clean/types.rs
+++ b/src/librustdoc/clean/types.rs
@@ -338,6 +338,7 @@ impl ExternalCrate {
 }
 
 /// Indicates where an external crate can be found.
+#[derive(Debug)]
 crate enum ExternalLocation {
     /// Remote URL root of the external crate
     Remote(String),
@@ -1539,23 +1540,10 @@ impl Type {
 
     /// Use this method to get the [DefId] of a [clean] AST node, including [PrimitiveType]s.
     ///
-    /// See [`Self::def_id_no_primitives`] for more.
-    ///
     /// [clean]: crate::clean
     crate fn def_id(&self, cache: &Cache) -> Option<DefId> {
         self.inner_def_id(Some(cache))
     }
-
-    /// Use this method to get the [`DefId`] of a [`clean`] AST node.
-    /// This will return [`None`] when called on a primitive [`clean::Type`].
-    /// Use [`Self::def_id`] if you want to include primitives.
-    ///
-    /// [`clean`]: crate::clean
-    /// [`clean::Type`]: crate::clean::Type
-    // FIXME: get rid of this function and always use `def_id`
-    crate fn def_id_no_primitives(&self) -> Option<DefId> {
-        self.inner_def_id(None)
-    }
 }
 
 /// A primitive (aka, builtin) type.
diff --git a/src/librustdoc/formats/cache.rs b/src/librustdoc/formats/cache.rs
index a8fef4a31780..53159709586c 100644
--- a/src/librustdoc/formats/cache.rs
+++ b/src/librustdoc/formats/cache.rs
@@ -303,7 +303,7 @@ impl<'a, 'tcx> DocFolder for CacheBuilder<'a, 'tcx> {
                             desc,
                             parent,
                             parent_idx: None,
-                            search_type: get_function_type_for_search(&item, self.tcx),
+                            search_type: get_function_type_for_search(&item, self.tcx, self.cache),
                             aliases: item.attrs.get_doc_aliases(),
                         });
                     }
diff --git a/src/librustdoc/html/render/search_index.rs b/src/librustdoc/html/render/search_index.rs
index 87138b9571c2..0ee67467c383 100644
--- a/src/librustdoc/html/render/search_index.rs
+++ b/src/librustdoc/html/render/search_index.rs
@@ -3,7 +3,7 @@ use std::collections::BTreeMap;
 
 use rustc_data_structures::fx::FxHashMap;
 use rustc_middle::ty::TyCtxt;
-use rustc_span::symbol::Symbol;
+use rustc_span::symbol::{kw, Symbol};
 use serde::ser::{Serialize, SerializeStruct, Serializer};
 
 use crate::clean;
@@ -33,7 +33,7 @@ crate fn build_index<'tcx>(krate: &clean::Crate, cache: &mut Cache, tcx: TyCtxt<
                 desc,
                 parent: Some(did),
                 parent_idx: None,
-                search_type: get_function_type_for_search(item, tcx),
+                search_type: get_function_type_for_search(item, tcx, &cache),
                 aliases: item.attrs.get_doc_aliases(),
             });
         }
@@ -188,11 +188,12 @@ crate fn build_index<'tcx>(krate: &clean::Crate, cache: &mut Cache, tcx: TyCtxt<
 crate fn get_function_type_for_search<'tcx>(
     item: &clean::Item,
     tcx: TyCtxt<'tcx>,
+    cache: &Cache,
 ) -> Option<IndexItemFunctionType> {
     let (mut inputs, mut output) = match *item.kind {
-        clean::FunctionItem(ref f) => get_fn_inputs_and_outputs(f, tcx),
-        clean::MethodItem(ref m, _) => get_fn_inputs_and_outputs(m, tcx),
-        clean::TyMethodItem(ref m) => get_fn_inputs_and_outputs(m, tcx),
+        clean::FunctionItem(ref f) => get_fn_inputs_and_outputs(f, tcx, cache),
+        clean::MethodItem(ref m, _) => get_fn_inputs_and_outputs(m, tcx, cache),
+        clean::TyMethodItem(ref m) => get_fn_inputs_and_outputs(m, tcx, cache),
         _ => return None,
     };
 
@@ -219,7 +220,8 @@ fn get_index_type_name(clean_type: &clean::Type) -> Option<Symbol> {
             let path = &bounds[0].trait_;
             Some(path.segments.last().unwrap().name)
         }
-        clean::Generic(s) => Some(s),
+        // We return an empty name because we don't care about the generic name itself.
+        clean::Generic(_) => Some(kw::Empty),
         clean::Primitive(ref p) => Some(p.as_sym()),
         clean::BorrowedRef { ref type_, .. } => get_index_type_name(type_),
         clean::BareFunction(_)
@@ -240,24 +242,27 @@ fn get_index_type_name(clean_type: &clean::Type) -> Option<Symbol> {
 ///
 /// Important note: It goes through generics recursively. So if you have
 /// `T: Option<Result<(), ()>>`, it'll go into `Option` and then into `Result`.
-#[instrument(level = "trace", skip(tcx, res))]
+#[instrument(level = "trace", skip(tcx, res, cache))]
 fn add_generics_and_bounds_as_types<'tcx>(
     generics: &Generics,
     arg: &Type,
     tcx: TyCtxt<'tcx>,
     recurse: usize,
     res: &mut Vec<TypeWithKind>,
+    cache: &Cache,
 ) {
     fn insert_ty(
         res: &mut Vec<TypeWithKind>,
         tcx: TyCtxt<'_>,
         ty: Type,
         mut generics: Vec<TypeWithKind>,
+        cache: &Cache,
     ) {
         let is_full_generic = ty.is_full_generic();
+        let generics_empty = generics.is_empty();
 
         if is_full_generic {
-            if generics.is_empty() {
+            if generics_empty {
                 // This is a type parameter with no trait bounds (for example: `T` in
                 // `fn f<T>(p: T)`, so not useful for the rustdoc search because we would end up
                 // with an empty type with an empty name. Let's just discard it.
@@ -304,14 +309,14 @@ fn add_generics_and_bounds_as_types<'tcx>(
             }
         }
         let mut index_ty = get_index_type(&ty, generics);
-        if index_ty.name.as_ref().map(|s| s.is_empty()).unwrap_or(true) {
+        if index_ty.name.as_ref().map(|s| s.is_empty() && generics_empty).unwrap_or(true) {
             return;
         }
         if is_full_generic {
             // We remove the name of the full generic because we have no use for it.
             index_ty.name = Some(String::new());
             res.push(TypeWithKind::from((index_ty, ItemType::Generic)));
-        } else if let Some(kind) = ty.def_id_no_primitives().map(|did| tcx.def_kind(did).into()) {
+        } else if let Some(kind) = ty.def_id(cache).map(|did| tcx.def_kind(did).into()) {
             res.push(TypeWithKind::from((index_ty, kind)));
         } else if ty.is_primitive() {
             // This is a primitive, let's store it as such.
@@ -330,9 +335,7 @@ fn add_generics_and_bounds_as_types<'tcx>(
     if let Type::Generic(arg_s) = *arg {
         // First we check if the bounds are in a `where` predicate...
         if let Some(where_pred) = generics.where_predicates.iter().find(|g| match g {
-            WherePredicate::BoundPredicate { ty, .. } => {
-                ty.def_id_no_primitives() == arg.def_id_no_primitives()
-            }
+            WherePredicate::BoundPredicate { ty, .. } => ty.def_id(cache) == arg.def_id(cache),
             _ => false,
         }) {
             let mut ty_generics = Vec::new();
@@ -348,6 +351,7 @@ fn add_generics_and_bounds_as_types<'tcx>(
                                     tcx,
                                     recurse + 1,
                                     &mut ty_generics,
+                                    cache,
                                 )
                             }
                             _ => {}
@@ -355,7 +359,7 @@ fn add_generics_and_bounds_as_types<'tcx>(
                     }
                 }
             }
-            insert_ty(res, tcx, arg.clone(), ty_generics);
+            insert_ty(res, tcx, arg.clone(), ty_generics, cache);
         }
         // Otherwise we check if the trait bounds are "inlined" like `T: Option<u32>`...
         if let Some(bound) = generics.params.iter().find(|g| g.is_type() && g.name == arg_s) {
@@ -369,10 +373,11 @@ fn add_generics_and_bounds_as_types<'tcx>(
                         tcx,
                         recurse + 1,
                         &mut ty_generics,
+                        cache,
                     );
                 }
             }
-            insert_ty(res, tcx, arg.clone(), ty_generics);
+            insert_ty(res, tcx, arg.clone(), ty_generics, cache);
         }
     } else {
         // This is not a type parameter. So for example if we have `T, U: Option<T>`, and we're
@@ -383,10 +388,17 @@ fn add_generics_and_bounds_as_types<'tcx>(
         let mut ty_generics = Vec::new();
         if let Some(arg_generics) = arg.generics() {
             for gen in arg_generics.iter() {
-                add_generics_and_bounds_as_types(generics, gen, tcx, recurse + 1, &mut ty_generics);
+                add_generics_and_bounds_as_types(
+                    generics,
+                    gen,
+                    tcx,
+                    recurse + 1,
+                    &mut ty_generics,
+                    cache,
+                );
             }
         }
-        insert_ty(res, tcx, arg.clone(), ty_generics);
+        insert_ty(res, tcx, arg.clone(), ty_generics, cache);
     }
 }
 
@@ -397,6 +409,7 @@ fn add_generics_and_bounds_as_types<'tcx>(
 fn get_fn_inputs_and_outputs<'tcx>(
     func: &Function,
     tcx: TyCtxt<'tcx>,
+    cache: &Cache,
 ) -> (Vec<TypeWithKind>, Vec<TypeWithKind>) {
     let decl = &func.decl;
     let generics = &func.generics;
@@ -407,12 +420,11 @@ fn get_fn_inputs_and_outputs<'tcx>(
             continue;
         }
         let mut args = Vec::new();
-        add_generics_and_bounds_as_types(generics, &arg.type_, tcx, 0, &mut args);
+        add_generics_and_bounds_as_types(generics, &arg.type_, tcx, 0, &mut args, cache);
         if !args.is_empty() {
             all_types.extend(args);
         } else {
-            if let Some(kind) = arg.type_.def_id_no_primitives().map(|did| tcx.def_kind(did).into())
-            {
+            if let Some(kind) = arg.type_.def_id(cache).map(|did| tcx.def_kind(did).into()) {
                 all_types.push(TypeWithKind::from((get_index_type(&arg.type_, vec![]), kind)));
             }
         }
@@ -421,11 +433,9 @@ fn get_fn_inputs_and_outputs<'tcx>(
     let mut ret_types = Vec::new();
     match decl.output {
         FnRetTy::Return(ref return_type) => {
-            add_generics_and_bounds_as_types(generics, return_type, tcx, 0, &mut ret_types);
+            add_generics_and_bounds_as_types(generics, return_type, tcx, 0, &mut ret_types, cache);
             if ret_types.is_empty() {
-                if let Some(kind) =
-                    return_type.def_id_no_primitives().map(|did| tcx.def_kind(did).into())
-                {
+                if let Some(kind) = return_type.def_id(cache).map(|did| tcx.def_kind(did).into()) {
                     ret_types.push(TypeWithKind::from((get_index_type(return_type, vec![]), kind)));
                 }
             }
diff --git a/src/librustdoc/passes/collect_trait_impls.rs b/src/librustdoc/passes/collect_trait_impls.rs
index 66ac612ea37c..53280b3df138 100644
--- a/src/librustdoc/passes/collect_trait_impls.rs
+++ b/src/librustdoc/passes/collect_trait_impls.rs
@@ -4,6 +4,7 @@
 use super::Pass;
 use crate::clean::*;
 use crate::core::DocContext;
+use crate::formats::cache::Cache;
 use crate::visit::DocVisitor;
 
 use rustc_data_structures::fx::{FxHashMap, FxHashSet};
@@ -57,14 +58,14 @@ crate fn collect_trait_impls(mut krate: Crate, cx: &mut DocContext<'_>) -> Crate
         }
     });
 
-    let mut cleaner = BadImplStripper { prims, items: crate_items };
+    let mut cleaner = BadImplStripper { prims, items: crate_items, cache: &cx.cache };
     let mut type_did_to_deref_target: FxHashMap<DefId, &Type> = FxHashMap::default();
 
     // Follow all `Deref` targets of included items and recursively add them as valid
     fn add_deref_target(
         cx: &DocContext<'_>,
         map: &FxHashMap<DefId, &Type>,
-        cleaner: &mut BadImplStripper,
+        cleaner: &mut BadImplStripper<'_>,
         type_did: DefId,
     ) {
         if let Some(target) = map.get(&type_did) {
@@ -102,7 +103,7 @@ crate fn collect_trait_impls(mut krate: Crate, cx: &mut DocContext<'_>) -> Crate
                 } else if let Some(did) = target.def_id(&cx.cache) {
                     cleaner.items.insert(did.into());
                 }
-                if let Some(for_did) = for_.def_id_no_primitives() {
+                if let Some(for_did) = for_.def_id(&cx.cache) {
                     if type_did_to_deref_target.insert(for_did, target).is_none() {
                         // Since only the `DefId` portion of the `Type` instances is known to be same for both the
                         // `Deref` target type and the impl for type positions, this map of types is keyed by
@@ -204,19 +205,20 @@ impl DocVisitor for ItemCollector {
     }
 }
 
-struct BadImplStripper {
+struct BadImplStripper<'a> {
     prims: FxHashSet<PrimitiveType>,
     items: FxHashSet<ItemId>,
+    cache: &'a Cache,
 }
 
-impl BadImplStripper {
+impl<'a> BadImplStripper<'a> {
     fn keep_impl(&self, ty: &Type, is_deref: bool) -> bool {
         if let Generic(_) = ty {
             // keep impls made on generics
             true
         } else if let Some(prim) = ty.primitive_type() {
             self.prims.contains(&prim)
-        } else if let Some(did) = ty.def_id_no_primitives() {
+        } else if let Some(did) = ty.def_id(self.cache) {
             is_deref || self.keep_impl_with_def_id(did.into())
         } else {
             false
diff --git a/src/librustdoc/passes/strip_hidden.rs b/src/librustdoc/passes/strip_hidden.rs
index e63534659add..e7a99ee7bfd8 100644
--- a/src/librustdoc/passes/strip_hidden.rs
+++ b/src/librustdoc/passes/strip_hidden.rs
@@ -15,7 +15,7 @@ crate const STRIP_HIDDEN: Pass = Pass {
 };
 
 /// Strip items marked `#[doc(hidden)]`
-crate fn strip_hidden(krate: clean::Crate, _: &mut DocContext<'_>) -> clean::Crate {
+crate fn strip_hidden(krate: clean::Crate, cx: &mut DocContext<'_>) -> clean::Crate {
     let mut retained = ItemIdSet::default();
 
     // strip all #[doc(hidden)] items
@@ -25,7 +25,7 @@ crate fn strip_hidden(krate: clean::Crate, _: &mut DocContext<'_>) -> clean::Cra
     };
 
     // strip all impls referencing stripped items
-    let mut stripper = ImplStripper { retained: &retained };
+    let mut stripper = ImplStripper { retained: &retained, cache: &cx.cache };
     stripper.fold_crate(krate)
 }
 
diff --git a/src/librustdoc/passes/strip_private.rs b/src/librustdoc/passes/strip_private.rs
index c6b5bec4692d..ef7e768a5114 100644
--- a/src/librustdoc/passes/strip_private.rs
+++ b/src/librustdoc/passes/strip_private.rs
@@ -29,6 +29,6 @@ crate fn strip_private(mut krate: clean::Crate, cx: &mut DocContext<'_>) -> clea
     }
 
     // strip all impls referencing private items
-    let mut stripper = ImplStripper { retained: &retained };
+    let mut stripper = ImplStripper { retained: &retained, cache: &cx.cache };
     stripper.fold_crate(krate)
 }
diff --git a/src/librustdoc/passes/stripper.rs b/src/librustdoc/passes/stripper.rs
index 7b07974ae01c..717dc078b343 100644
--- a/src/librustdoc/passes/stripper.rs
+++ b/src/librustdoc/passes/stripper.rs
@@ -5,6 +5,7 @@ use std::mem;
 
 use crate::clean::{self, Item, ItemIdSet};
 use crate::fold::{strip_item, DocFolder};
+use crate::formats::cache::Cache;
 
 crate struct Stripper<'a> {
     crate retained: &'a mut ItemIdSet,
@@ -118,6 +119,7 @@ impl<'a> DocFolder for Stripper<'a> {
 /// This stripper discards all impls which reference stripped items
 crate struct ImplStripper<'a> {
     crate retained: &'a ItemIdSet,
+    crate cache: &'a Cache,
 }
 
 impl<'a> DocFolder for ImplStripper<'a> {
@@ -127,7 +129,7 @@ impl<'a> DocFolder for ImplStripper<'a> {
             if imp.trait_.is_none() && imp.items.is_empty() {
                 return None;
             }
-            if let Some(did) = imp.for_.def_id_no_primitives() {
+            if let Some(did) = imp.for_.def_id(self.cache) {
                 if did.is_local() && !imp.for_.is_assoc_ty() && !self.retained.contains(&did.into())
                 {
                     debug!("ImplStripper: impl item for stripped type; removing");
@@ -142,7 +144,7 @@ impl<'a> DocFolder for ImplStripper<'a> {
             }
             if let Some(generics) = imp.trait_.as_ref().and_then(|t| t.generics()) {
                 for typaram in generics {
-                    if let Some(did) = typaram.def_id_no_primitives() {
+                    if let Some(did) = typaram.def_id(self.cache) {
                         if did.is_local() && !self.retained.contains(&did.into()) {
                             debug!(
                                 "ImplStripper: stripped item in trait's generics; removing impl"