diff --git a/include/npcomp/Conversion/Passes.td b/include/npcomp/Conversion/Passes.td
index b43d20760..563e42f42 100644
--- a/include/npcomp/Conversion/Passes.td
+++ b/include/npcomp/Conversion/Passes.td
@@ -42,7 +42,7 @@ def ConvertNumpyToTCF : Pass<"convert-numpy-to-tcf", "FuncOp"> {
 // TCFToTCP
 //===----------------------------------------------------------------------===//
 
-def ConvertTCFToLinalg : Pass<"convert-tcf-to-linalg", "ModuleOp"> {
+def ConvertTCFToLinalg : Pass<"convert-tcf-to-linalg", "FuncOp"> {
   let summary = "Convert TCF to Linalg";
   let description = [{
     The intention is for this pass to convert mainly to linalg named ops.
@@ -57,7 +57,7 @@ def ConvertTCFToLinalg : Pass<"convert-tcf-to-linalg", "ModuleOp"> {
 // TCFToStd
 //===----------------------------------------------------------------------===//
 
-def ConvertTCFToStd : Pass<"convert-tcf-to-std", "ModuleOp"> {
+def ConvertTCFToStd : Pass<"convert-tcf-to-std", "FuncOp"> {
   let summary = "Convert TCF to Std";
   let constructor = "mlir::NPCOMP::createConvertTCFToStdPass()";
 }
@@ -66,7 +66,7 @@ def ConvertTCFToStd : Pass<"convert-tcf-to-std", "ModuleOp"> {
 // TCFToTCP
 //===----------------------------------------------------------------------===//
 
-def ConvertTCFToTCP : Pass<"convert-tcf-to-tcp", "ModuleOp"> {
+def ConvertTCFToTCP : Pass<"convert-tcf-to-tcp", "FuncOp"> {
   let summary = "Convert TCF to TCP";
   let constructor = "mlir::NPCOMP::createConvertTCFToTCPPass()";
 }
diff --git a/include/npcomp/Conversion/TCFToLinalg/TCFToLinalg.h b/include/npcomp/Conversion/TCFToLinalg/TCFToLinalg.h
index 1bbfc588c..8c4eca694 100644
--- a/include/npcomp/Conversion/TCFToLinalg/TCFToLinalg.h
+++ b/include/npcomp/Conversion/TCFToLinalg/TCFToLinalg.h
@@ -14,7 +14,7 @@
 
 namespace mlir {
 namespace NPCOMP {
-std::unique_ptr<OperationPass<ModuleOp>> createConvertTCFToLinalgPass();
+std::unique_ptr<OperationPass<FuncOp>> createConvertTCFToLinalgPass();
 }
 } // namespace mlir
 
diff --git a/include/npcomp/Conversion/TCFToStd/TCFToStd.h b/include/npcomp/Conversion/TCFToStd/TCFToStd.h
index 96588d0b8..1a0095522 100644
--- a/include/npcomp/Conversion/TCFToStd/TCFToStd.h
+++ b/include/npcomp/Conversion/TCFToStd/TCFToStd.h
@@ -14,7 +14,7 @@
 
 namespace mlir {
 namespace NPCOMP {
-std::unique_ptr<OperationPass<ModuleOp>> createConvertTCFToStdPass();
+std::unique_ptr<OperationPass<FuncOp>> createConvertTCFToStdPass();
 }
 } // namespace mlir
 
diff --git a/include/npcomp/Conversion/TCFToTCP/TCFToTCP.h b/include/npcomp/Conversion/TCFToTCP/TCFToTCP.h
index 1947b74ba..d93049d1c 100644
--- a/include/npcomp/Conversion/TCFToTCP/TCFToTCP.h
+++ b/include/npcomp/Conversion/TCFToTCP/TCFToTCP.h
@@ -14,7 +14,7 @@
 
 namespace mlir {
 namespace NPCOMP {
-std::unique_ptr<OperationPass<ModuleOp>> createConvertTCFToTCPPass();
+std::unique_ptr<OperationPass<FuncOp>> createConvertTCFToTCPPass();
 }
 } // namespace mlir
 
diff --git a/lib/Conversion/TCFToLinalg/TCFToLinalg.cpp b/lib/Conversion/TCFToLinalg/TCFToLinalg.cpp
index 35c9f54fa..2494744a3 100644
--- a/lib/Conversion/TCFToLinalg/TCFToLinalg.cpp
+++ b/lib/Conversion/TCFToLinalg/TCFToLinalg.cpp
@@ -84,8 +84,7 @@ public:
   }
 
   void runOnOperation() override {
-    ModuleOp module = getOperation();
-    (void)applyPatternsAndFoldGreedily(module, getPatterns());
+    (void)applyPatternsAndFoldGreedily(getOperation(), getPatterns());
   }
 
   FrozenRewritePatternList getPatterns() {
@@ -97,7 +96,7 @@ public:
 };
 } // namespace
 
-std::unique_ptr<OperationPass<ModuleOp>>
+std::unique_ptr<OperationPass<FuncOp>>
 mlir::NPCOMP::createConvertTCFToLinalgPass() {
   return std::make_unique<ConvertTCFToLinalg>();
 }
diff --git a/lib/Conversion/TCFToStd/TCFToStd.cpp b/lib/Conversion/TCFToStd/TCFToStd.cpp
index 9ddb89743..506f41512 100644
--- a/lib/Conversion/TCFToStd/TCFToStd.cpp
+++ b/lib/Conversion/TCFToStd/TCFToStd.cpp
@@ -139,8 +139,7 @@ public:
   }
 
   void runOnOperation() override {
-    ModuleOp module = getOperation();
-    (void)applyPatternsAndFoldGreedily(module, getPatterns());
+    (void)applyPatternsAndFoldGreedily(getOperation(), getPatterns());
   }
 
   FrozenRewritePatternList getPatterns() {
@@ -156,7 +155,7 @@ public:
 };
 } // namespace
 
-std::unique_ptr<OperationPass<ModuleOp>>
+std::unique_ptr<OperationPass<FuncOp>>
 mlir::NPCOMP::createConvertTCFToStdPass() {
   return std::make_unique<ConvertTCFToStd>();
 }
diff --git a/lib/Conversion/TCFToTCP/TCFToTCP.cpp b/lib/Conversion/TCFToTCP/TCFToTCP.cpp
index dba2dd0c3..334ffc7dd 100644
--- a/lib/Conversion/TCFToTCP/TCFToTCP.cpp
+++ b/lib/Conversion/TCFToTCP/TCFToTCP.cpp
@@ -29,8 +29,7 @@ public:
   }
 
   void runOnOperation() override {
-    ModuleOp module = getOperation();
-    (void)applyPatternsAndFoldGreedily(module, getPatterns());
+    (void)applyPatternsAndFoldGreedily(getOperation(), getPatterns());
   }
 
   FrozenRewritePatternList getPatterns() {
@@ -43,7 +42,7 @@ public:
 };
 } // namespace
 
-std::unique_ptr<OperationPass<ModuleOp>>
+std::unique_ptr<OperationPass<FuncOp>>
 mlir::NPCOMP::createConvertTCFToTCPPass() {
   return std::make_unique<ConvertTCFToTCP>();
 }
diff --git a/lib/RefBackend/RefBackend.cpp b/lib/RefBackend/RefBackend.cpp
index 67498e1f7..f2e10dd2f 100644
--- a/lib/RefBackend/RefBackend.cpp
+++ b/lib/RefBackend/RefBackend.cpp
@@ -243,7 +243,7 @@ void mlir::NPCOMP::createRefBackendLoweringPipeline(
   // Run some upstream bufferization passes to finish bufferization.
   pm.addNestedPass<FuncOp>(createStdBufferizePass());
   pm.addNestedPass<FuncOp>(createSCFBufferizePass());
-  pm.addPass(createLinalgBufferizePass());
+  pm.addNestedPass<FuncOp>(createLinalgBufferizePass());
   pm.addPass(createFuncBufferizePass());
 
   // TODO: Do buffer deallocation. We should be able to just drop in the
@@ -306,9 +306,9 @@ void mlir::NPCOMP::createTCFRefBackendLoweringPipeline(
   //
   // TCP does not. So we need to reify the broadcasting and error checking.
   // These all run at the module level.
-  pm.addPass(createConvertTCFToStdPass());
-  pm.addPass(createConvertTCFToLinalgPass());
-  pm.addPass(createConvertTCFToTCPPass());
+  pm.addNestedPass<FuncOp>(createConvertTCFToStdPass());
+  pm.addNestedPass<FuncOp>(createConvertTCFToLinalgPass());
+  pm.addNestedPass<FuncOp>(createConvertTCFToTCPPass());
 
   createRefBackendLoweringPipeline(pm, options);
 }