diff --git a/llvm/include/llvm/Transforms/IPO/Attributor.h b/llvm/include/llvm/Transforms/IPO/Attributor.h
--- a/llvm/include/llvm/Transforms/IPO/Attributor.h
+++ b/llvm/include/llvm/Transforms/IPO/Attributor.h
@@ -591,6 +591,13 @@
     return AG.getAnalysis<AAManager>(F);
   }
 
+  /// Return true if \p Arg is involved in a must-tail call, thus the argument
+  /// of the caller or callee.
+  bool isInvolvedInMustTailCall(const Argument &Arg) const {
+    return FunctionsCalledViaMustTail.count(Arg.getParent()) ||
+           FunctionsWithMustTailCall.count(Arg.getParent());
+  }
+
   /// Return the analysis result from a pass \p AP for function \p F.
   template <typename AP>
   typename AP::Result *getAnalysisResultForFunction(const Function &F) {
@@ -621,6 +628,12 @@
   /// A map from functions to their instructions that may read or write memory.
   FuncRWInstsMapTy FuncRWInstsMap;
 
+  /// Functions called by a `musttail` call.
+  SmallPtrSet<Function *, 8> FunctionsCalledViaMustTail;
+
+  /// Functions containing a `musttail` call.
+  SmallPtrSet<Function *, 8> FunctionsWithMustTailCall;
+
   /// The datalayout used in the module.
   const DataLayout &DL;
 
diff --git a/llvm/lib/Transforms/IPO/Attributor.cpp b/llvm/lib/Transforms/IPO/Attributor.cpp
--- a/llvm/lib/Transforms/IPO/Attributor.cpp
+++ b/llvm/lib/Transforms/IPO/Attributor.cpp
@@ -4062,10 +4062,20 @@
 struct AAAlignArgument final
     : AAArgumentFromCallSiteArgumentsAndMustBeExecutedContext<AAAlign,
                                                               AAAlignImpl> {
-  AAAlignArgument(const IRPosition &IRP)
-      : AAArgumentFromCallSiteArgumentsAndMustBeExecutedContext<AAAlign,
-                                                                AAAlignImpl>(
-            IRP) {}
+  using Base =
+      AAArgumentFromCallSiteArgumentsAndMustBeExecutedContext<AAAlign,
+                                                              AAAlignImpl>;
+  AAAlignArgument(const IRPosition &IRP) : Base(IRP) {}
+
+  /// See AbstractAttribute::initialize(...).
+  void initialize(Attributor &A) override {
+    Base::initialize(A);
+    // If the associated argument is involved in a must-tail call we give up
+    // because we would need to keep the argument alignments of caller and
+    // callee in-sync. Just does not seem worth the trouble right now.
+    if (A.getInfoCache().isInvolvedInMustTailCall(*getAssociatedArgument()))
+      indicatePessimisticFixpoint();
+  }
 
   /// See AbstractAttribute::trackStatistics()
   void trackStatistics() const override { STATS_DECLTRACK_ARG_ATTR(aligned) }
@@ -8308,11 +8318,12 @@
              "New call site/base instruction type needs to be known in the "
              "Attributor.");
       break;
-    case Instruction::Load:
-      // The alignment of a pointer is interesting for loads.
-    case Instruction::Store:
-      // The alignment of a pointer is interesting for stores.
     case Instruction::Call:
+      if (cast<CallInst>(I).isMustTailCall()) {
+        InfoCache.FunctionsWithMustTailCall.insert(&F);
+        InfoCache.FunctionsCalledViaMustTail.insert(
+            cast<CallInst>(I).getCalledFunction());
+      }
     case Instruction::CallBr:
     case Instruction::Invoke:
     case Instruction::CleanupRet:
@@ -8322,6 +8333,10 @@
     case Instruction::Br:
     case Instruction::Resume:
     case Instruction::Ret:
+    case Instruction::Load:
+      // The alignment of a pointer is interesting for loads.
+    case Instruction::Store:
+      // The alignment of a pointer is interesting for stores.
       IsInterestingOpcode = true;
     }
     if (IsInterestingOpcode)
@@ -8356,6 +8371,15 @@
   if (F.isDeclaration())
     return;
 
+  // In non-module runs we need to look at the call sites of a function to
+  // determine if it is part of a must-tail call edge. This will influence what
+  // attributes we can derive.
+  if (!isModulePass() && !InfoCache.FunctionsCalledViaMustTail.count(&F))
+    for (const Use &U : F.uses())
+      if (ImmutableCallSite ICS = ImmutableCallSite(U.getUser()))
+        if (ICS.isCallee(&U) && ICS.isMustTailCall())
+          InfoCache.FunctionsCalledViaMustTail.insert(&F);
+
   IRPosition FPos = IRPosition::function(F);
 
   // Check for dead BasicBlocks in every function.
diff --git a/llvm/test/Transforms/Attributor/ArgumentPromotion/musttail.ll b/llvm/test/Transforms/Attributor/ArgumentPromotion/musttail.ll
--- a/llvm/test/Transforms/Attributor/ArgumentPromotion/musttail.ll
+++ b/llvm/test/Transforms/Attributor/ArgumentPromotion/musttail.ll
@@ -1,5 +1,5 @@
 ; NOTE: Assertions have been autogenerated by utils/update_test_checks.py UTC_ARGS: --function-signature --scrub-attributes
-; RUN: opt -S -passes=attributor -aa-pipeline='basic-aa' -attributor-disable=false -attributor-max-iterations-verify -attributor-max-iterations=1 < %s | FileCheck %s
+; RUN: opt -S -passes=attributor -aa-pipeline='basic-aa' -attributor-disable=false -attributor-max-iterations-verify -attributor-max-iterations=2 < %s | FileCheck %s
 ; PR36543
 
 ; Don't promote arguments of musttail callee
diff --git a/llvm/test/Transforms/Attributor/align.ll b/llvm/test/Transforms/Attributor/align.ll
--- a/llvm/test/Transforms/Attributor/align.ll
+++ b/llvm/test/Transforms/Attributor/align.ll
@@ -552,6 +552,23 @@
   store i8 0, i8* %bc
   ret void
 }
+
+; Make sure we do not annotate the callee of a must-tail call with an alignment
+; we cannot also put on the caller.
+@cnd = external global i1
+define i32 @musttail_callee_1(i32* %p) {
+  %v = load i32, i32* %p, align 32
+  ret i32 %v
+}
+define i32 @musttail_caller_1(i32* %p) {
+  %c = load i1, i1* @cnd
+  br i1 %c, label %mt, label %exit
+mt:
+  %v = musttail call i32 @musttail_callee_1(i32* %p)
+  ret i32 %v
+exit:
+  ret i32 0
+}
 ; UTC_ARGS: --disable
 
 attributes #0 = { nounwind uwtable noinline }