diff --git a/java/kotlin-extractor2/src/main/kotlin/entities/Types.kt b/java/kotlin-extractor2/src/main/kotlin/entities/Types.kt
index ae98127eef979..f54b723b90f4f 100644
--- a/java/kotlin-extractor2/src/main/kotlin/entities/Types.kt
+++ b/java/kotlin-extractor2/src/main/kotlin/entities/Types.kt
@@ -9,8 +9,13 @@ private fun KotlinUsesExtractor.useClassType(
     c: KaClassType
 ): TypeResults {
     // TODO: this cast is unsafe; .symbol is actually a KaClassLikeSymbol
-    val javaResult = TypeResult(addClassLabel(c.symbol as KaClassSymbol) /* , TODO, TODO */)
-    val kotlinResult = TypeResult(fakeKotlinType() /* , "TODO", "TODO" */)
+    val classId = addClassLabel(c.symbol as KaClassSymbol)
+    val javaResult = TypeResult(classId /* , TODO, TODO */)
+    val kotlinTypeId =
+        tw.getLabelFor<DbKt_class_type>("@\"kt_class{$classId}\"") {
+            tw.writeKt_class_types(it, classId)
+        }
+    val kotlinResult = TypeResult(kotlinTypeId /* , "TODO", "TODO" */)
     return TypeResults(javaResult, kotlinResult)
 }
 
@@ -44,8 +49,8 @@ private fun KotlinUsesExtractor.extractJavaErrorType(): TypeResult<DbErrortype>
 private fun KotlinUsesExtractor.extractErrorType(): TypeResults {
     val javaResult = extractJavaErrorType()
     val kotlinTypeId =
-        tw.getLabelFor<DbKt_nullable_type>("@\"errorKotlinType\"") {
-            tw.writeKt_nullable_types(it, javaResult.id)
+        tw.getLabelFor<DbKt_error_type>("@\"errorKotlinType\"") {
+            tw.writeKt_error_types(it)
         }
     return TypeResults(
         javaResult,
@@ -53,23 +58,6 @@ private fun KotlinUsesExtractor.extractErrorType(): TypeResults {
     )
 }
 
-// TODO
-fun KotlinUsesExtractor.fakeKotlinType(): Label<out DbKt_type> {
-    val fakeKotlinPackageId: Label<DbPackage> =
-        tw.getLabelFor("@\"FakeKotlinPackage\"", { tw.writePackages(it, "fake.kotlin") })
-    val fakeKotlinClassId: Label<DbClassorinterface> =
-        tw.getLabelFor(
-            "@\"FakeKotlinClass\"",
-            { tw.writeClasses_or_interfaces(it, "FakeKotlinClass", fakeKotlinPackageId, it) }
-        )
-    val fakeKotlinTypeId: Label<DbKt_nullable_type> =
-        tw.getLabelFor(
-            "@\"FakeKotlinType\"",
-            { tw.writeKt_nullable_types(it, fakeKotlinClassId) }
-        )
-    return fakeKotlinTypeId
-}
-
 /*
 OLD: KE1
     // `args` can be null to describe a raw generic type.
diff --git a/java/ql/lib/config/semmlecode.dbscheme b/java/ql/lib/config/semmlecode.dbscheme
index e0fd7f76ab869..d162a1bc3f652 100644
--- a/java/ql/lib/config/semmlecode.dbscheme
+++ b/java/ql/lib/config/semmlecode.dbscheme
@@ -461,23 +461,41 @@ type_companion_object(
   unique int companion_object: @classorinterface ref
 );
 
-kt_nullable_types(
-  unique int id: @kt_nullable_type,
+/**
+ * `id` is the Kotlin type for the non-nullable class type `classid`.
+ */
+kt_class_types(
+  unique int id: @kt_class_type,
   int classid: @reftype ref
 )
 
-kt_notnull_types(
-  unique int id: @kt_notnull_type,
-  int classid: @reftype ref
+/**
+ * `id` is the Kotlin type that is the same as `kttypeid`, but is nullable.
+ */
+kt_nullable_types(
+  unique int id: @kt_nullable_type,
+  int kttypeid: @kt_type ref
 )
 
+/**
+ * `id` is the Kotlin type that is the alias called `name` of `kttypeid`.
+ * That is, it has been defined by `typealias name = kttypeid`.
+ */
 kt_type_alias(
   unique int id: @kt_type_alias,
   string name: string ref,
   int kttypeid: @kt_type ref
 )
 
-@kt_type = @kt_nullable_type | @kt_notnull_type
+/**
+ * A `kt_error_type` is used when the extractor is unable to extract a type
+ * correctly for some reason.
+ */
+kt_error_types(
+  unique int id: @kt_error_type
+)
+
+@kt_type = @kt_class_type | @kt_nullable_type | @kt_type_alias | @kt_error_type
 
 /**
  * This holds if `id` is an `interface`, rather than a `class`.
diff --git a/java/ql/lib/semmle/code/java/KotlinType.qll b/java/ql/lib/semmle/code/java/KotlinType.qll
index 3e5597c5579d8..159484bdc5fb4 100644
--- a/java/ql/lib/semmle/code/java/KotlinType.qll
+++ b/java/ql/lib/semmle/code/java/KotlinType.qll
@@ -8,28 +8,31 @@ class KotlinType extends Element, @kt_type { }
 
 class KotlinNullableType extends KotlinType, @kt_nullable_type {
   override string toString() {
-    exists(RefType javaType |
-      kt_nullable_types(this, javaType) and
-      result = "Kotlin nullable " + javaType.toString()
+    exists(KotlinType ktType |
+      kt_nullable_types(this, ktType) and
+      result = ktType.toString() + "?"
     )
   }
 
   override string getAPrimaryQlClass() { result = "KotlinNullableType" }
 }
 
-class KotlinNotnullType extends KotlinType, @kt_notnull_type {
-  override string toString() {
-    exists(RefType javaType |
-      kt_notnull_types(this, javaType) and
-      result = "Kotlin not-null " + javaType.toString()
-    )
-  }
+class KotlinClassType extends KotlinType, @kt_class_type {
+  override string toString() { result = this.getClass().toString() }
 
   override string getAPrimaryQlClass() { result = "KotlinNotnullType" }
+
+  RefType getClass() { kt_class_types(this, result) }
 }
 
-class KotlinTypeAlias extends Element, @kt_type_alias {
+class KotlinTypeAlias extends KotlinType, @kt_type_alias {
   override string getAPrimaryQlClass() { result = "KotlinTypeAlias" }
 
+  override string toString() {
+    result = "{" + this.getKotlinType().toString() + "}" + this.getName()
+  }
+
+  override string getName() { kt_type_alias(this, result, _) }
+
   KotlinType getKotlinType() { kt_type_alias(this, _, result) }
 }