diff --git a/lib/ImportModelFromC/HeaderToModel.cpp b/lib/ImportModelFromC/HeaderToModel.cpp
index ee619f677..bea18ab59 100644
--- a/lib/ImportModelFromC/HeaderToModel.cpp
+++ b/lib/ImportModelFromC/HeaderToModel.cpp
@@ -459,7 +459,7 @@ DeclVisitor::getTypeByNameOrID(llvm::StringRef Name, TypeKind::Values Kind) {
     std::istringstream TheStream(ID);
     TheStream >> TypeID;
 
-    auto KeyType = model::Type::Key{ Kind, TypeID };
+    auto KeyType = model::Type::Key{ TypeID, Kind };
 
     auto TheType = Model->getTypePath(KeyType);
     if (TheType.get())
@@ -941,9 +941,11 @@ bool DeclVisitor::VisitTypedefDecl(const TypedefDecl *D) {
     llvm::erase_if(Model->Types(), [&](UpcastablePointer<model::Type> &P) {
       return P.get()->ID() == (*Type)->ID();
     });
-  }
 
-  Model->recordNewType(std::move(TypeTypedef));
+    Model->Types().insert(std::move(TypeTypedef));
+  } else {
+    Model->recordNewType(std::move(TypeTypedef));
+  }
 
   return true;
 }
@@ -1014,9 +1016,11 @@ bool DeclVisitor::VisitFunctionPrototype(const FunctionProtoType *FP,
     llvm::erase_if(Model->Types(), [&](UpcastablePointer<model::Type> &P) {
       return P.get()->ID() == (*Type)->ID();
     });
-  }
 
-  Model->recordNewType(std::move(NewType));
+    Model->Types().insert(std::move(NewType));
+  } else {
+    Model->recordNewType(std::move(NewType));
+  }
 
   return true;
 }
@@ -1126,18 +1130,23 @@ bool DeclVisitor::handleStructType(const clang::RecordDecl *RD) {
   // TODO: Can this be calculated/fetched automatically?
   Struct->Size() = CurrentOffset;
 
-  if (AnalysisOption == ImportModelFromCOption::EditType) {
+  switch (AnalysisOption) {
+  case ImportModelFromCOption::EditType:
     // Remove old and add new type with the same ID.
     llvm::erase_if(Model->Types(), [&](UpcastablePointer<model::Type> &P) {
       return P.get()->ID() == (*Type)->ID();
     });
-  }
+    Model->Types().insert(std::move(NewType));
+    break;
 
-  if (AnalysisOption != ImportModelFromCOption::EditFunctionPrototype)
-    Model->recordNewType(std::move(NewType));
-
-  if (AnalysisOption == ImportModelFromCOption::EditFunctionPrototype)
+  case ImportModelFromCOption::EditFunctionPrototype:
     MultiRegisterReturnValue = ReturnValues;
+    break;
+
+  case ImportModelFromCOption::AddType:
+    Model->recordNewType(std::move(NewType));
+    break;
+  }
 
   return true;
 }
@@ -1187,9 +1196,11 @@ bool DeclVisitor::handleUnionType(const clang::RecordDecl *RD) {
     llvm::erase_if(Model->Types(), [&](UpcastablePointer<model::Type> &P) {
       return P.get()->ID() == (*Type)->ID();
     });
+    Model->Types().insert(std::move(NewType));
+  } else {
+    Model->recordNewType(std::move(NewType));
   }
 
-  Model->recordNewType(std::move(NewType));
   return true;
 }
 
@@ -1279,9 +1290,12 @@ bool DeclVisitor::VisitEnumDecl(const EnumDecl *D) {
     llvm::erase_if(Model->Types(), [&](UpcastablePointer<model::Type> &P) {
       return P.get()->ID() == (*Type)->ID();
     });
+
+    Model->Types().insert(std::move(NewType));
+  } else {
+    Model->recordNewType(std::move(NewType));
   }
 
-  Model->recordNewType(std::move(NewType));
   return true;
 }
 
diff --git a/tests/unit/llvm-lit-tests/CheckDLA.ll b/tests/unit/llvm-lit-tests/CheckDLA.ll
index 0b8ea12cf..8a0c881d8 100644
--- a/tests/unit/llvm-lit-tests/CheckDLA.ll
+++ b/tests/unit/llvm-lit-tests/CheckDLA.ll
@@ -2,7 +2,7 @@
 ; Copyright rev.ng Labs Srl. See LICENSE.md for details.
 ;
 
-; RUN: %revngopt %s -S --dla --model-type-id-seed=0xDEADBEEF -o - | revng model dump | revng model compare %s.yml -
+; RUN: %revngopt %s -S --dla -o - | revng model dump | revng model compare %s.yml -
 ; This file is meant to be used to test that the DLA is able to merge the
 ; recovered type information with an already existing model.
 ; In particular, in this file all functions and indirect calls share the same