diff --git a/mlir/include/mlir/Dialect/Linalg/ComprehensiveBufferize/ComprehensiveBufferize.h b/mlir/include/mlir/Dialect/Linalg/ComprehensiveBufferize/ComprehensiveBufferize.h
--- a/mlir/include/mlir/Dialect/Linalg/ComprehensiveBufferize/ComprehensiveBufferize.h
+++ b/mlir/include/mlir/Dialect/Linalg/ComprehensiveBufferize/ComprehensiveBufferize.h
@@ -16,14 +16,21 @@
 namespace linalg {
 namespace comprehensive_bufferize {
 
+class BufferizationAliasInfo;
 struct BufferizationOptions;
 class BufferizationState;
 
+/// Analyze `op` and its nested ops. Bufferization decisions are stored in
+/// `state`.
+LogicalResult analyzeOp(Operation *op, BufferizationState &state);
+
 /// Bufferize the given operation. Reuses an existing BufferizationState object.
+/// If `runAnalysis` is set to false, all OpOperands bufferize out-of-place.
 /// This function overload is for internal usage only.
 LogicalResult runComprehensiveBufferize(Operation *op,
                                         const BufferizationOptions &options,
-                                        BufferizationState &state);
+                                        BufferizationState &state,
+                                        bool runAnalysis = true);
 
 /// Bufferize the given operation.
 LogicalResult
diff --git a/mlir/lib/Dialect/Linalg/ComprehensiveBufferize/ComprehensiveBufferize.cpp b/mlir/lib/Dialect/Linalg/ComprehensiveBufferize/ComprehensiveBufferize.cpp
--- a/mlir/lib/Dialect/Linalg/ComprehensiveBufferize/ComprehensiveBufferize.cpp
+++ b/mlir/lib/Dialect/Linalg/ComprehensiveBufferize/ComprehensiveBufferize.cpp
@@ -618,13 +618,12 @@
   return success();
 }
 
-LogicalResult mlir::linalg::comprehensive_bufferize::runComprehensiveBufferize(
-    Operation *op, const BufferizationOptions &options,
-    BufferizationState &state) {
-
-  IRRewriter rewriter(op->getContext());
+LogicalResult
+mlir::linalg::comprehensive_bufferize::analyzeOp(Operation *op,
+                                                 BufferizationState &state) {
   DominanceInfo domInfo(op);
   BufferizationAliasInfo &aliasInfo = state.getAliasInfo();
+  const BufferizationOptions &options = state.getOptions();
 
   if (failed(checkAliasInfoConsistency(op, domInfo, state, aliasInfo)))
     return failure();
@@ -647,10 +646,18 @@
   }
 
   // Annotate operations if we only want to report the analysis.
-  if (options.testAnalysisOnly) {
+  if (options.testAnalysisOnly)
     annotateOpsWithBufferizationMarkers(op, aliasInfo, state);
-    return success();
-  }
+
+  return success();
+}
+
+LogicalResult mlir::linalg::comprehensive_bufferize::runComprehensiveBufferize(
+    Operation *op, const BufferizationOptions &options,
+    BufferizationState &state, bool runAnalysis) {
+  if (runAnalysis)
+    if (failed(analyzeOp(op, state)))
+      return failure();
 
   // Bufferize the op and its nested ops.
   OwningRewritePatternList patterns(op->getContext());
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
@@ -842,6 +842,8 @@
   // inplace. Therefore, we just bufferize funcOp as if none of its results were
   // inplaceable, detect which operands are cloned internally and decide what to
   // do at call sites.
+
+  // Analyze ops.
   for (FuncOp funcOp : moduleState.orderedFuncOps) {
     // No body => no analysis.
     if (funcOp.body().empty())
@@ -854,8 +856,8 @@
     // Gather equivalence info for CallOps.
     equivalenceAnalysis(funcOp, aliasInfo, moduleState);
 
-    // Analyze and bufferize funcOp.
-    if (failed(runComprehensiveBufferize(funcOp, *options, state)))
+    // Analyze funcOp.
+    if (failed(analyzeOp(funcOp, state)))
       return failure();
 
     // Add annotations to function arguments.
@@ -866,6 +868,18 @@
   if (options->testAnalysisOnly)
     return success();
 
+  // Bufferize function bodies.
+  for (FuncOp funcOp : moduleState.orderedFuncOps) {
+    // No body => no analysis.
+    if (funcOp.body().empty())
+      continue;
+
+    if (failed(runComprehensiveBufferize(funcOp, *options, state,
+                                         /*runAnalysis=*/false)))
+      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.