Index: lib/Transforms/InstCombine/InstCombineSelect.cpp
===================================================================
--- lib/Transforms/InstCombine/InstCombineSelect.cpp
+++ lib/Transforms/InstCombine/InstCombineSelect.cpp
@@ -1450,6 +1450,20 @@
     }
   }
 
+  // If we can compute the condition, there's no need for a select.
+  // Like the above fold, we are attempting to reduce compile-time cost by
+  // putting this fold here with limitations rather than in InstSimplify.
+  // The motivation for this call into value tracking is to take advantage of
+  // the assumption cache, so make sure that is populated.
+  if (!CondVal->getType()->isVectorTy() && !AC.assumptions().empty()) {
+    APInt KnownOne(1, 0), KnownZero(1, 0);
+    computeKnownBits(CondVal, KnownZero, KnownOne, 0, &SI);
+    if (KnownOne == 1)
+      return replaceInstUsesWith(SI, TrueVal);
+    if (KnownZero == 1)
+      return replaceInstUsesWith(SI, FalseVal);
+  }
+
   if (Instruction *BitCastSel = foldSelectCmpBitcasts(SI, *Builder))
     return BitCastSel;
 
Index: test/Transforms/InstCombine/select.ll
===================================================================
--- test/Transforms/InstCombine/select.ll
+++ test/Transforms/InstCombine/select.ll
@@ -1332,3 +1332,27 @@
   ret <4 x i32> %sel
 }
 
+declare void @llvm.assume(i1)
+
+define i8 @assume_cond_true(i1 %cond, i8 %x, i8 %y) {
+; CHECK-LABEL: @assume_cond_true(
+; CHECK-NEXT:    call void @llvm.assume(i1 %cond)
+; CHECK-NEXT:    ret i8 %x
+;
+  call void @llvm.assume(i1 %cond)
+  %sel = select i1 %cond, i8 %x, i8 %y
+  ret i8 %sel
+}
+
+define i8 @assume_cond_false(i1 %cond, i8 %x, i8 %y) {
+; CHECK-LABEL: @assume_cond_false(
+; CHECK-NEXT:    [[NOTCOND:%.*]] = xor i1 %cond, true
+; CHECK-NEXT:    call void @llvm.assume(i1 [[NOTCOND]])
+; CHECK-NEXT:    ret i8 %y
+;
+  %notcond = icmp eq i1 %cond, false
+  call void @llvm.assume(i1 %notcond)
+  %sel = select i1 %cond, i8 %x, i8 %y
+  ret i8 %sel
+}
+
Index: test/Transforms/InstSimplify/select.ll
===================================================================
--- test/Transforms/InstSimplify/select.ll
+++ test/Transforms/InstSimplify/select.ll
@@ -402,7 +402,8 @@
   ret i32* %sel
 }
 
-; FIXME: If the condition is known, we don't need to select.
+; If the condition is known, we don't need to select, but we're not
+; doing this fold here to avoid compile-time cost.
 
 declare void @llvm.assume(i1)