diff --git a/compiler/builtin_lib_types.m b/compiler/builtin_lib_types.m
index c68678f37..96cd42af9 100644
--- a/compiler/builtin_lib_types.m
+++ b/compiler/builtin_lib_types.m
@@ -75,9 +75,11 @@
     %
 :- pred type_is_type_info_or_ctor_type(mer_type::in) is semidet.
 
-    % Check whether a type is the `typeclass_info' type.
+    % Check whether a type is represents either a type_info or typeclass_info,
+    % or their type_ctor_info and base_typeclass_info components.
+    % These are the types of the variables that can occur in rtti_varmaps.
     %
-:- pred type_is_typeclass_info_type(mer_type::in) is semidet.
+:- pred type_is_rtti_relevant_type(mer_type::in) is semidet.
 
 %---------------------------------------------------------------------------%
 %
@@ -297,17 +299,29 @@ build_type_info_type(Type) = TypeInfoType :-
 
 %---------------------%
 
-type_is_type_info_or_ctor_type(TypeInfoType) :-
-    type_to_ctor_and_args(TypeInfoType, TypeCtor, []),
+type_is_type_info_or_ctor_type(Type) :-
+    type_to_ctor_and_args(Type, TypeCtor, []),
     TypeCtor = type_ctor(qualified(ModuleName, TypeName), 0),
-    ModuleName = mercury_private_builtin_module,
     ( TypeName = "type_info"
     ; TypeName = "type_ctor_info"
-    ).
+    ),
+    ModuleName = mercury_private_builtin_module.
 
-type_is_typeclass_info_type(TypeClassInfoType) :-
-    type_to_ctor_and_args(TypeClassInfoType, TypeCtor, []),
-    TypeCtor = type_ctor(qualified(ModuleName, "typeclass_info"), 0),
+type_is_rtti_relevant_type(Type) :-
+    type_to_ctor_and_args(Type, TypeCtor, []),
+    TypeCtor = type_ctor(qualified(ModuleName, TypeName), 0),
+    % NOTE polymorphism_type_class_info.m actually creates
+    % base_typeclass_info variables with their types being
+    % "typeclass_info", NOT "base_typeclass_info". However, other parts
+    % of the compiler do look out for them under the type name
+    % "base_typeclass_info", probably because this used to be true
+    % in the past. Including that name in the test here is preparing
+    % for a possible return to that state of affairs.
+    ( TypeName = "type_info"
+    ; TypeName = "type_ctor_info"
+    ; TypeName = "typeclass_info"
+    ; TypeName = "base_typeclass_info"
+    ),
     ModuleName = mercury_private_builtin_module.
 
 %---------------------------------------------------------------------------%
diff --git a/compiler/float_regs.m b/compiler/float_regs.m
index 9829dc83e..3a8314c3e 100644
--- a/compiler/float_regs.m
+++ b/compiler/float_regs.m
@@ -1259,11 +1259,7 @@ insert_reg_wrappers_method_call(ClassId, MethodProcNum, Vars0, Vars,
 take_non_rtti_types_from_tail([], []).
 take_non_rtti_types_from_tail([Type | Types0], Types) :-
     take_non_rtti_types_from_tail(Types0, TypesTail),
-    ( if
-        ( type_is_typeclass_info_type(Type)
-        ; type_is_type_info_or_ctor_type(Type)
-        )
-    then
+    ( if type_is_rtti_relevant_type(Type) then
         Types = TypesTail
     else
         Types = [Type | TypesTail]
diff --git a/compiler/saved_vars.m b/compiler/saved_vars.m
index da4bcd48b..572f34418 100644
--- a/compiler/saved_vars.m
+++ b/compiler/saved_vars.m
@@ -222,7 +222,7 @@ saved_vars_in_conj([Goal0 | Goals0], Goals, NonLocals, !SlotInfo) :-
                 ok_to_duplicate(Feature) = yes
             )
         ),
-        slot_info_ok_to_duplicate_var(!.SlotInfo, Var),
+        slot_info_ok_to_duplicate_var(!.SlotInfo, Var) = yes,
         skip_constant_constructs(Goals0, Constants, OtherGoals),
         OtherGoals = [First | _Rest],
         can_push(Var, First) = yes
@@ -666,17 +666,24 @@ saved_vars_rename_var(Var, NewVar, Substitution, !SlotInfo) :-
     % it is possible that liveness.m will want to refer to the rtti_varmaps
     % to calculate which type_infos are live (see the comments at the top
     % of liveness.m). If we duplicated any type_info variables here,
-    % then this could cause problems because the rtti_varmaps would not
+    % then this could cause problems, because the rtti_varmaps would not
     % be able to be kept consistent. Therefore we don't allow type_infos
-    % to be duplicated when TypeInfoLiveness is set.
+    % to be duplicated when TypeInfoLiveness is set. The same reasoning
+    % applies to typeclass_info types.
     %
-:- pred slot_info_ok_to_duplicate_var(slot_info::in, prog_var::in) is semidet.
+:- func slot_info_ok_to_duplicate_var(slot_info, prog_var) = bool.
 
-slot_info_ok_to_duplicate_var(SlotInfo, Var) :-
+slot_info_ok_to_duplicate_var(SlotInfo, Var) = OkToDuplicate :-
     SlotInfo = slot_info(VarTable, _, TypeInfoLiveness),
-    TypeInfoLiveness = yes,
     lookup_var_type(VarTable, Var, Type),
-    not type_is_type_info_or_ctor_type(Type).
+    ( if
+        TypeInfoLiveness = yes,
+        type_is_rtti_relevant_type(Type)
+    then
+        OkToDuplicate = no
+    else
+        OkToDuplicate = yes
+    ).
 
 %-----------------------------------------------------------------------------%
 :- end_module ll_backend.saved_vars.