diff --git a/cpp/ql/src/semmle/code/cpp/internal/ResolveClass.qll b/cpp/ql/src/semmle/code/cpp/internal/ResolveClass.qll
index c3cde4c4346c..eaefc8196cc8 100644
--- a/cpp/ql/src/semmle/code/cpp/internal/ResolveClass.qll
+++ b/cpp/ql/src/semmle/code/cpp/internal/ResolveClass.qll
@@ -1,23 +1,31 @@
 import semmle.code.cpp.Type
 
-/** Holds if `d` is a complete class named `name`. */
+pragma[noinline]
+private string getTopLevelClassName(@usertype c) {
+  isClass(c) and
+  usertypes(c, result, _) and
+  not namespacembrs(_, c) and // not in a namespace
+  not member(_, _, c) and // not in some structure
+  not class_instantiation(c, _) // not a template instantiation
+}
+
+/** Holds if `d` is a unique complete class named `name`. */
 pragma[noinline]
 private predicate existsCompleteWithName(string name, @usertype d) {
-  isClass(d) and
   is_complete(d) and
-  usertypes(d, name, _)
+  name = getTopLevelClassName(d) and
+  strictcount(@usertype other | is_complete(other) and getTopLevelClassName(other) = name) = 1
 }
 
 /** Holds if `c` is an incomplete class named `name`. */
 pragma[noinline]
 private predicate existsIncompleteWithName(string name, @usertype c) {
-  isClass(c) and
   not is_complete(c) and
-  usertypes(c, name, _)
+  name = getTopLevelClassName(c)
 }
 
 /**
- * Holds if `c` is an imcomplete class, and there exists a complete class `d`
+ * Holds if `c` is an imcomplete class, and there exists a unique complete class `d`
  * with the same name.
  */
 private predicate hasCompleteTwin(@usertype c, @usertype d) {
@@ -30,10 +38,8 @@ private predicate hasCompleteTwin(@usertype c, @usertype d) {
 import Cached
 cached private module Cached {
   /**
-   * If `c` is incomplete, and there exists a complete class with the same name,
-   * then the result is that complete class. Otherwise, the result is `c`. If
-   * multiple complete classes have the same name, this predicate may have
-   * multiple results.
+   * If `c` is incomplete, and there exists a unique complete class with the same name,
+   * then the result is that complete class. Otherwise, the result is `c`.
    */
   cached @usertype resolveClass(@usertype c) {
     hasCompleteTwin(c, result)
diff --git a/cpp/ql/test/library-tests/structs/compatible_cpp/b1.cpp b/cpp/ql/test/library-tests/structs/compatible_cpp/b1.cpp
index c7d839b4874d..760147d60ff0 100644
--- a/cpp/ql/test/library-tests/structs/compatible_cpp/b1.cpp
+++ b/cpp/ql/test/library-tests/structs/compatible_cpp/b1.cpp
@@ -24,3 +24,9 @@ class Damson {
   int damson_x;
   void foo();
 };
+
+namespace unrelated {
+  class AppleCompatible {
+    long apple_x;
+  };
+}
diff --git a/cpp/ql/test/library-tests/structs/compatible_cpp/compatible.expected b/cpp/ql/test/library-tests/structs/compatible_cpp/compatible.expected
index 4b631dde98b4..326fea4210f8 100644
--- a/cpp/ql/test/library-tests/structs/compatible_cpp/compatible.expected
+++ b/cpp/ql/test/library-tests/structs/compatible_cpp/compatible.expected
@@ -32,6 +32,9 @@
 | b1.cpp:23:7:23:12 | Damson | 5 members | 2 locations | 1 | foo |
 | b1.cpp:23:7:23:12 | Damson | 5 members | 2 locations | 2 | operator= |
 | b1.cpp:23:7:23:12 | Damson | 5 members | 2 locations | 3 | operator= |
+| b1.cpp:29:9:29:23 | AppleCompatible | 3 members | 1 locations | 0 | apple_x |
+| b1.cpp:29:9:29:23 | AppleCompatible | 3 members | 1 locations | 1 | operator= |
+| b1.cpp:29:9:29:23 | AppleCompatible | 3 members | 1 locations | 2 | operator= |
 | b2.cpp:2:7:2:21 | AppleCompatible | 3 members | 2 locations | 0 | apple_x |
 | b2.cpp:2:7:2:21 | AppleCompatible | 3 members | 2 locations | 1 | operator= |
 | b2.cpp:2:7:2:21 | AppleCompatible | 3 members | 2 locations | 2 | operator= |
diff --git a/cpp/ql/test/library-tests/structs/compatible_cpp/compatible_types.expected b/cpp/ql/test/library-tests/structs/compatible_cpp/compatible_types.expected
index df2a178f6674..f9446f1b19a6 100644
--- a/cpp/ql/test/library-tests/structs/compatible_cpp/compatible_types.expected
+++ b/cpp/ql/test/library-tests/structs/compatible_cpp/compatible_types.expected
@@ -10,6 +10,7 @@
 | b1.cpp:11:7:11:22 | BananaCompatible | 0 | file://:0:0:0:0 | int | 1 types |
 | b1.cpp:16:7:16:12 | Cherry | 0 | file://:0:0:0:0 | int | 1 types |
 | b1.cpp:23:7:23:12 | Damson | 0 | file://:0:0:0:0 | int | 1 types |
+| b1.cpp:29:9:29:23 | AppleCompatible | 0 | file://:0:0:0:0 | long | 1 types |
 | b2.cpp:2:7:2:21 | AppleCompatible | 0 | file://:0:0:0:0 | int | 1 types |
 | b2.cpp:9:7:9:22 | BananaCompatible | 0 | file://:0:0:0:0 | int | 1 types |
 | b2.cpp:14:7:14:12 | Cherry | 0 | file://:0:0:0:0 | short | 1 types |
diff --git a/cpp/ql/test/library-tests/structs/incomplete_definition/pointerbasetype.expected b/cpp/ql/test/library-tests/structs/incomplete_definition/pointerbasetype.expected
index 98a672ad4353..801306a572ab 100644
--- a/cpp/ql/test/library-tests/structs/incomplete_definition/pointerbasetype.expected
+++ b/cpp/ql/test/library-tests/structs/incomplete_definition/pointerbasetype.expected
@@ -1,2 +1,6 @@
 | a.h:5:8:5:13 | cheese | y.cpp:4:8:4:10 | Foo | 3 |
 | x.cpp:3:6:3:10 | bar_x | a.h:4:8:4:10 | Bar | 3 |
+| x.cpp:19:6:19:10 | foo_x | y.cpp:4:8:4:10 | Foo | 3 |
+| x.cpp:23:5:23:17 | templateField | x.cpp:6:10:6:12 | Foo | 3 |
+| x.cpp:23:5:23:17 | templateField | x.cpp:12:9:12:11 | Foo | 3 |
+| x.cpp:26:18:26:29 | template_foo | x.cpp:22:7:22:14 | Template<Foo *> | 0 |
diff --git a/cpp/ql/test/library-tests/structs/incomplete_definition/x.cpp b/cpp/ql/test/library-tests/structs/incomplete_definition/x.cpp
index 5b2a352e3dd7..ab5eb9474553 100644
--- a/cpp/ql/test/library-tests/structs/incomplete_definition/x.cpp
+++ b/cpp/ql/test/library-tests/structs/incomplete_definition/x.cpp
@@ -1,3 +1,31 @@
 #include "a.h"
 
 Bar *bar_x;
+
+namespace unrelated {
+  struct Foo {
+    short val;
+  };
+}
+
+struct ContainsAnotherFoo {
+  class Foo {
+    long val;
+  };
+};
+
+// The type of `foo_x` should not refer to any of the above classes, none of
+// which are named `Foo` in the global scope.
+Foo *foo_x;
+
+template<typename T>
+class Template {
+  T templateField;
+};
+
+Template<Foo *> *template_foo;
+
+// Instantiation of the template with unrelated classes named `Foo` should not
+// get mixed up with the instantiation above.
+template class Template<unrelated::Foo *>;
+template class Template<ContainsAnotherFoo::Foo *>;
diff --git a/cpp/ql/test/library-tests/structs/qualified_names/c1.cpp b/cpp/ql/test/library-tests/structs/qualified_names/c1.cpp
new file mode 100644
index 000000000000..f72303701213
--- /dev/null
+++ b/cpp/ql/test/library-tests/structs/qualified_names/c1.cpp
@@ -0,0 +1,9 @@
+#include "header.h"
+
+struct MultipleDefsButSameHeader {
+  int i;
+};
+
+struct OneDefInDifferentFile {
+  int i;
+};
diff --git a/cpp/ql/test/library-tests/structs/qualified_names/c2.cpp b/cpp/ql/test/library-tests/structs/qualified_names/c2.cpp
new file mode 100644
index 000000000000..be5380566150
--- /dev/null
+++ b/cpp/ql/test/library-tests/structs/qualified_names/c2.cpp
@@ -0,0 +1,6 @@
+#include "header.h"
+
+struct MultipleDefsButSameHeader {
+  char char1;
+  char char2;
+};
diff --git a/cpp/ql/test/library-tests/structs/qualified_names/decls.cpp b/cpp/ql/test/library-tests/structs/qualified_names/decls.cpp
new file mode 100644
index 000000000000..c6cde7b00b90
--- /dev/null
+++ b/cpp/ql/test/library-tests/structs/qualified_names/decls.cpp
@@ -0,0 +1,5 @@
+namespace foo {
+  class C;
+
+  C *x;
+}
diff --git a/cpp/ql/test/library-tests/structs/qualified_names/defs.cpp b/cpp/ql/test/library-tests/structs/qualified_names/defs.cpp
new file mode 100644
index 000000000000..095f84126044
--- /dev/null
+++ b/cpp/ql/test/library-tests/structs/qualified_names/defs.cpp
@@ -0,0 +1,29 @@
+namespace foo {
+  class C {
+  };
+}
+
+namespace bar {
+  class C {
+  };
+}
+
+class DefinedAndDeclared {
+};
+
+// Despite this declaration being present, the variable below is associated
+// with the definition above rather than this declaration.
+class DefinedAndDeclared;
+
+DefinedAndDeclared *definedAndDeclared;
+
+#include "header.h"
+
+// Because there are multiple definitions of `MultipleDefsButSameHeader`, the
+// type of this variable will refer to the declaration in `header.h` rather
+// than any of the definitions.
+MultipleDefsButSameHeader *mdbsh;
+
+// Because there is only one definition of `OneDefInDifferentFile`, the type of
+// this variable will refer to that definition.
+OneDefInDifferentFile *odidf;
diff --git a/cpp/ql/test/library-tests/structs/qualified_names/header.h b/cpp/ql/test/library-tests/structs/qualified_names/header.h
new file mode 100644
index 000000000000..d410b0d35333
--- /dev/null
+++ b/cpp/ql/test/library-tests/structs/qualified_names/header.h
@@ -0,0 +1,3 @@
+struct MultipleDefsButSameHeader;
+
+struct OneDefInDifferentFile;
diff --git a/cpp/ql/test/library-tests/structs/qualified_names/pointerBaseType.expected b/cpp/ql/test/library-tests/structs/qualified_names/pointerBaseType.expected
new file mode 100644
index 000000000000..1573f1c446e2
--- /dev/null
+++ b/cpp/ql/test/library-tests/structs/qualified_names/pointerBaseType.expected
@@ -0,0 +1,4 @@
+| decls.cpp:4:6:4:6 | x | decls.cpp:2:9:2:9 | C |
+| defs.cpp:18:21:18:38 | definedAndDeclared | defs.cpp:11:7:11:24 | DefinedAndDeclared |
+| defs.cpp:25:28:25:32 | mdbsh | header.h:1:8:1:32 | MultipleDefsButSameHeader |
+| defs.cpp:29:24:29:28 | odidf | c1.cpp:7:8:7:28 | OneDefInDifferentFile |
diff --git a/cpp/ql/test/library-tests/structs/qualified_names/pointerBaseType.ql b/cpp/ql/test/library-tests/structs/qualified_names/pointerBaseType.ql
new file mode 100644
index 000000000000..b2aeaee63488
--- /dev/null
+++ b/cpp/ql/test/library-tests/structs/qualified_names/pointerBaseType.ql
@@ -0,0 +1,5 @@
+import cpp
+
+from Variable x
+where exists(x.getFile().getRelativePath())
+select x, x.getType().(PointerType).getBaseType()
diff --git a/cpp/ql/test/library-tests/templates/isfromtemplateinstantiation/isfromtemplateinstantiation.expected b/cpp/ql/test/library-tests/templates/isfromtemplateinstantiation/isfromtemplateinstantiation.expected
index 4d2706e2e952..dc73e749a4cd 100644
--- a/cpp/ql/test/library-tests/templates/isfromtemplateinstantiation/isfromtemplateinstantiation.expected
+++ b/cpp/ql/test/library-tests/templates/isfromtemplateinstantiation/isfromtemplateinstantiation.expected
@@ -116,32 +116,13 @@
 | isfromtemplateinstantiation.cpp:134:29:134:29 | Outer<int>::operator=(const Outer<int> &) | isfromtemplateinstantiation.cpp:134:29:134:33 | Outer<int> |
 | isfromtemplateinstantiation.cpp:134:29:134:29 | declaration of operator= | isfromtemplateinstantiation.cpp:134:29:134:33 | Outer<int> |
 | isfromtemplateinstantiation.cpp:134:29:134:29 | declaration of operator= | isfromtemplateinstantiation.cpp:134:29:134:33 | Outer<int> |
-| isfromtemplateinstantiation.cpp:135:31:135:31 | Outer<T>::Inner<long>::operator=(Inner<long> &&) | isfromtemplateinstantiation.cpp:134:29:134:33 | Outer<int> |
 | isfromtemplateinstantiation.cpp:135:31:135:31 | Outer<T>::Inner<long>::operator=(Inner<long> &&) | isfromtemplateinstantiation.cpp:135:31:135:35 | Inner<long> |
-| isfromtemplateinstantiation.cpp:135:31:135:31 | Outer<T>::Inner<long>::operator=(const Inner<long> &) | isfromtemplateinstantiation.cpp:134:29:134:33 | Outer<int> |
 | isfromtemplateinstantiation.cpp:135:31:135:31 | Outer<T>::Inner<long>::operator=(const Inner<long> &) | isfromtemplateinstantiation.cpp:135:31:135:35 | Inner<long> |
-| isfromtemplateinstantiation.cpp:135:31:135:31 | Outer<int>::Inner<long>::operator=(Inner<long> &&) | isfromtemplateinstantiation.cpp:134:29:134:33 | Outer<int> |
-| isfromtemplateinstantiation.cpp:135:31:135:31 | Outer<int>::Inner<long>::operator=(Inner<long> &&) | isfromtemplateinstantiation.cpp:135:31:135:35 | Inner<long> |
-| isfromtemplateinstantiation.cpp:135:31:135:31 | Outer<int>::Inner<long>::operator=(const Inner<long> &) | isfromtemplateinstantiation.cpp:134:29:134:33 | Outer<int> |
-| isfromtemplateinstantiation.cpp:135:31:135:31 | Outer<int>::Inner<long>::operator=(const Inner<long> &) | isfromtemplateinstantiation.cpp:135:31:135:35 | Inner<long> |
-| isfromtemplateinstantiation.cpp:135:31:135:31 | declaration of operator= | isfromtemplateinstantiation.cpp:134:29:134:33 | Outer<int> |
-| isfromtemplateinstantiation.cpp:135:31:135:31 | declaration of operator= | isfromtemplateinstantiation.cpp:134:29:134:33 | Outer<int> |
 | isfromtemplateinstantiation.cpp:135:31:135:31 | declaration of operator= | isfromtemplateinstantiation.cpp:135:31:135:35 | Inner<long> |
 | isfromtemplateinstantiation.cpp:135:31:135:31 | declaration of operator= | isfromtemplateinstantiation.cpp:135:31:135:35 | Inner<long> |
-| isfromtemplateinstantiation.cpp:135:31:135:35 | Inner<U> | isfromtemplateinstantiation.cpp:134:29:134:33 | Outer<int> |
-| isfromtemplateinstantiation.cpp:135:31:135:35 | Inner<long> | isfromtemplateinstantiation.cpp:134:29:134:33 | Outer<int> |
-| isfromtemplateinstantiation.cpp:135:31:135:35 | definition of Inner<U> | isfromtemplateinstantiation.cpp:134:29:134:33 | Outer<int> |
-| isfromtemplateinstantiation.cpp:136:7:136:7 | definition of x | isfromtemplateinstantiation.cpp:134:29:134:33 | Outer<int> |
-| isfromtemplateinstantiation.cpp:136:7:136:7 | definition of x | isfromtemplateinstantiation.cpp:134:29:134:33 | Outer<int> |
 | isfromtemplateinstantiation.cpp:136:7:136:7 | definition of x | isfromtemplateinstantiation.cpp:135:31:135:35 | Inner<long> |
-| isfromtemplateinstantiation.cpp:136:7:136:7 | x | isfromtemplateinstantiation.cpp:134:29:134:33 | Outer<int> |
-| isfromtemplateinstantiation.cpp:136:7:136:7 | x | isfromtemplateinstantiation.cpp:134:29:134:33 | Outer<int> |
 | isfromtemplateinstantiation.cpp:136:7:136:7 | x | isfromtemplateinstantiation.cpp:135:31:135:35 | Inner<long> |
-| isfromtemplateinstantiation.cpp:137:7:137:7 | definition of y | isfromtemplateinstantiation.cpp:134:29:134:33 | Outer<int> |
-| isfromtemplateinstantiation.cpp:137:7:137:7 | definition of y | isfromtemplateinstantiation.cpp:134:29:134:33 | Outer<int> |
 | isfromtemplateinstantiation.cpp:137:7:137:7 | definition of y | isfromtemplateinstantiation.cpp:135:31:135:35 | Inner<long> |
-| isfromtemplateinstantiation.cpp:137:7:137:7 | y | isfromtemplateinstantiation.cpp:134:29:134:33 | Outer<int> |
-| isfromtemplateinstantiation.cpp:137:7:137:7 | y | isfromtemplateinstantiation.cpp:134:29:134:33 | Outer<int> |
 | isfromtemplateinstantiation.cpp:137:7:137:7 | y | isfromtemplateinstantiation.cpp:135:31:135:35 | Inner<long> |
 | load.cpp:13:7:13:7 | basic_text_iprimitive<std_istream_mockup>::basic_text_iprimitive(basic_text_iprimitive<std_istream_mockup> &&) | load.cpp:13:7:13:27 | basic_text_iprimitive<std_istream_mockup> |
 | load.cpp:13:7:13:7 | basic_text_iprimitive<std_istream_mockup>::basic_text_iprimitive(const basic_text_iprimitive<std_istream_mockup> &) | load.cpp:13:7:13:27 | basic_text_iprimitive<std_istream_mockup> |
diff --git a/cpp/ql/test/library-tests/templates/isfromtemplateinstantiation/isfromuninstantiatedtemplate.expected b/cpp/ql/test/library-tests/templates/isfromtemplateinstantiation/isfromuninstantiatedtemplate.expected
index 38fda5364eef..74a096dff1aa 100644
--- a/cpp/ql/test/library-tests/templates/isfromtemplateinstantiation/isfromuninstantiatedtemplate.expected
+++ b/cpp/ql/test/library-tests/templates/isfromtemplateinstantiation/isfromuninstantiatedtemplate.expected
@@ -3,6 +3,7 @@ isFromUninstantiatedTemplate
 | file://:0:0:0:0 | 0 | isfromtemplateinstantiation.cpp:77:26:77:45 | AnotherTemplateClass<T> |
 | file://:0:0:0:0 | (int)... | isfromtemplateinstantiation.cpp:77:26:77:45 | AnotherTemplateClass<T> |
 | file://:0:0:0:0 | (int)... | isfromtemplateinstantiation.cpp:77:26:77:45 | AnotherTemplateClass<T> |
+| file://:0:0:0:0 | Inner<U> | file://:0:0:0:0 | Inner<U> |
 | file://:0:0:0:0 | declaration of 1st parameter | isfromtemplateinstantiation.cpp:134:29:134:33 | Outer<T> |
 | file://:0:0:0:0 | declaration of 1st parameter | isfromtemplateinstantiation.cpp:134:29:134:33 | Outer<T> |
 | file://:0:0:0:0 | initializer for MyClassEnumConst | isfromtemplateinstantiation.cpp:77:26:77:45 | AnotherTemplateClass<T> |
@@ -433,15 +434,15 @@ isFromUninstantiatedTemplate
 | isfromtemplateinstantiation.cpp:135:31:135:31 | declaration of operator= | I | T | DeclarationEntry |  |
 | isfromtemplateinstantiation.cpp:135:31:135:31 | operator= | I | T | Declaration |  |
 | isfromtemplateinstantiation.cpp:135:31:135:31 | operator= | I | T | Declaration |  |
-| isfromtemplateinstantiation.cpp:135:31:135:35 | Inner<U> | I | T | Declaration |  |
+| isfromtemplateinstantiation.cpp:135:31:135:35 | Inner<U> |  | T | Declaration |  |
 | isfromtemplateinstantiation.cpp:135:31:135:35 | Inner<long> | I | T | Declaration |  |
+| isfromtemplateinstantiation.cpp:136:7:136:7 | definition of x |  | T | Definition |  |
 | isfromtemplateinstantiation.cpp:136:7:136:7 | definition of x | I | T | Definition |  |
-| isfromtemplateinstantiation.cpp:136:7:136:7 | definition of x | I | T | Definition |  |
-| isfromtemplateinstantiation.cpp:136:7:136:7 | x | I | T | Declaration |  |
+| isfromtemplateinstantiation.cpp:136:7:136:7 | x |  | T | Declaration |  |
 | isfromtemplateinstantiation.cpp:136:7:136:7 | x | I | T | Declaration |  |
+| isfromtemplateinstantiation.cpp:137:7:137:7 | definition of y |  | T | Definition |  |
 | isfromtemplateinstantiation.cpp:137:7:137:7 | definition of y | I | T | Definition |  |
-| isfromtemplateinstantiation.cpp:137:7:137:7 | definition of y | I | T | Definition |  |
-| isfromtemplateinstantiation.cpp:137:7:137:7 | y | I | T | Declaration |  |
+| isfromtemplateinstantiation.cpp:137:7:137:7 | y |  | T | Declaration |  |
 | isfromtemplateinstantiation.cpp:137:7:137:7 | y | I | T | Declaration |  |
 | isfromtemplateinstantiation.cpp:144:28:144:56 | incomplete_never_instantiated<T> |  | T | Declaration |  |
 | isfromtemplateinstantiation.cpp:146:28:146:45 | never_instantiated<T> |  | T | Declaration |  |