diff --git a/mlir/lib/Dialect/Linalg/ComprehensiveBufferize/ModuleBufferization.cpp b/mlir/lib/Dialect/Linalg/ComprehensiveBufferize/ModuleBufferization.cpp
--- a/mlir/lib/Dialect/Linalg/ComprehensiveBufferize/ModuleBufferization.cpp
+++ b/mlir/lib/Dialect/Linalg/ComprehensiveBufferize/ModuleBufferization.cpp
@@ -1033,14 +1033,13 @@
     // Now analyzing function.
     moduleState.startFunctionAnalysis(funcOp);
 
+    // Gather equivalence info for CallOps.
+    equivalenceAnalysis(funcOp, aliasInfo, moduleState);
+
     // Analyze funcOp.
     if (failed(analyzeOp(funcOp, analysisState)))
       return failure();
 
-    // Gather equivalence info for CallOps.
-    // TODO: Make this a post-analysis step.
-    equivalenceAnalysis(funcOp, aliasInfo, moduleState);
-
     // Mark op as fully analyzed.
     moduleState.analyzedFuncOps[funcOp] = FuncOpAnalysisState::Analyzed;
 
@@ -1052,23 +1051,21 @@
   if (options.testAnalysisOnly)
     return success();
 
-  // Bufferize function bodies.
+  // Bufferize functions.
   for (FuncOp funcOp : moduleState.orderedFuncOps) {
     // No body => no analysis.
-    if (funcOp.getBody().empty())
-      continue;
-
-    if (failed(bufferizeOp(funcOp, bufferizationState)))
-      return failure();
-  }
+    if (!funcOp.getBody().empty())
+      if (failed(bufferizeOp(funcOp, bufferizationState)))
+        return failure();
 
-  // Bufferize function boundaries.
-  for (FuncOp funcOp : moduleState.orderedFuncOps) {
     // Note: It would be good to apply cleanups here but we cannot as aliasInfo
     // would be invalidated.
     if (failed(bufferizeFuncOpBoundary(funcOp, rewriter, bufferizationState)))
       return failure();
+  }
 
+  // Check result.
+  for (FuncOp funcOp : moduleState.orderedFuncOps) {
     if (!options.allowReturnAllocs &&
         llvm::any_of(funcOp.getFunctionType().getResults(), [](Type t) {
           return t.isa<MemRefType, UnrankedMemRefType>();
diff --git a/mlir/test/Dialect/Linalg/comprehensive-module-bufferize-invalid.mlir b/mlir/test/Dialect/Linalg/comprehensive-module-bufferize-invalid.mlir
--- a/mlir/test/Dialect/Linalg/comprehensive-module-bufferize-invalid.mlir
+++ b/mlir/test/Dialect/Linalg/comprehensive-module-bufferize-invalid.mlir
@@ -212,11 +212,10 @@
 
 // -----
 
+// expected-error @+1 {{cannot bufferize bodiless function that returns a tensor}}
 func private @foo(%t : tensor<?xf32>) -> (f32, tensor<?xf32>, f32)
 
 func @call_to_unknown_tensor_returning_func(%t : tensor<?xf32>) {
-  // expected-error @+2 {{call to FuncOp that returns non-equivalent tensors not supported}}
-  // expected-error @+1 {{op was not bufferized}}
   call @foo(%t) : (tensor<?xf32>) -> (f32, tensor<?xf32>, f32)
   return
 }