diff --git a/source/opt/optimizer.cpp b/source/opt/optimizer.cpp
index 8aed7bc1..e697e436 100644
--- a/source/opt/optimizer.cpp
+++ b/source/opt/optimizer.cpp
@@ -102,12 +102,15 @@ Optimizer& Optimizer::RegisterLegalizationPasses() {
           .RegisterPass(CreateLocalSingleBlockLoadStoreElimPass())
           .RegisterPass(CreateLocalSingleStoreElimPass())
           .RegisterPass(CreateLocalMultiStoreElimPass())
+          // Propagate constants to get as many constant conditions on branches
+          // as possible.
+          .RegisterPass(CreateCCPPass())
+          .RegisterPass(CreateDeadBranchElimPass())
           // Copy propagate members.  Cleans up code sequences generated by
-          // scalar replacement.
+          // scalar replacement.  Also important for removing OpPhi nodes.
           .RegisterPass(CreateSimplificationPass())
           // May need loop unrolling here see
           // https://github.com/Microsoft/DirectXShaderCompiler/pull/930
-          .RegisterPass(CreateDeadBranchElimPass())
           // Get rid of unused code that contain traces of illegal code
           // or unused references to unbound external objects
           .RegisterPass(CreateDeadInsertElimPass())
@@ -130,6 +133,7 @@ Optimizer& Optimizer::RegisterPerformancePasses() {
       .RegisterPass(CreateInsertExtractElimPass())
       .RegisterPass(CreateDeadInsertElimPass())
       .RegisterPass(CreateDeadBranchElimPass())
+      .RegisterPass(CreateSimplificationPass())
       .RegisterPass(CreateIfConversionPass())
       .RegisterPass(CreateAggressiveDCEPass())
       .RegisterPass(CreateBlockMergePass())