diff --git a/llvm/tools/llvm-exegesis/lib/ParallelSnippetGenerator.cpp b/llvm/tools/llvm-exegesis/lib/ParallelSnippetGenerator.cpp
index 0d284af12c762..c2691fea6344d 100644
--- a/llvm/tools/llvm-exegesis/lib/ParallelSnippetGenerator.cpp
+++ b/llvm/tools/llvm-exegesis/lib/ParallelSnippetGenerator.cpp
@@ -325,7 +325,7 @@ ParallelSnippetGenerator::generateCodeTemplates(
   SmallVector<RegRandomizationStrategy, 3> Strategies;
   if (HasTiedOperands || NumUntiedUseRegs >= 3)
     Strategies.push_back(RegRandomizationStrategy::PickRandomRegs);
-  if (HasTiedOperands || NumUntiedUseRegs >= 2)
+  if (NumUntiedUseRegs >= 2)
     Strategies.push_back(RegRandomizationStrategy::SingleStaticRegPerOperand);
   Strategies.push_back(RegRandomizationStrategy::SingleStaticReg);
   for (RegRandomizationStrategy S : Strategies) {
diff --git a/llvm/unittests/tools/llvm-exegesis/X86/SnippetGeneratorTest.cpp b/llvm/unittests/tools/llvm-exegesis/X86/SnippetGeneratorTest.cpp
index b6d25f0c0b92b..3200ec50d2d5b 100644
--- a/llvm/unittests/tools/llvm-exegesis/X86/SnippetGeneratorTest.cpp
+++ b/llvm/unittests/tools/llvm-exegesis/X86/SnippetGeneratorTest.cpp
@@ -251,7 +251,7 @@ TEST_F(X86ParallelSnippetGeneratorTest, ReadAfterWrite_CMOV32rr) {
   // - hasAliasingRegisters
   const unsigned Opcode = X86::CMOV32rr;
   const auto CodeTemplates = checkAndGetCodeTemplates(Opcode);
-  ASSERT_THAT(CodeTemplates, SizeIs(3));
+  ASSERT_THAT(CodeTemplates, SizeIs(2));
   for (const auto &CT : CodeTemplates) {
     EXPECT_THAT(CT.Info, HasSubstr("avoiding Read-After-Write issue"));
     EXPECT_THAT(CT.Execution, ExecutionMode::UNKNOWN);