Index: lib/Analysis/InstructionSimplify.cpp
===================================================================
--- lib/Analysis/InstructionSimplify.cpp
+++ lib/Analysis/InstructionSimplify.cpp
@@ -3708,6 +3708,16 @@
           simplifySelectWithICmpCond(CondVal, TrueVal, FalseVal, Q, MaxRecurse))
     return V;
 
+  // If we can compute the condition, there's no need for a select.
+  if (CondVal->getType()->getPrimitiveSizeInBits() == 1) {
+    APInt KnownOne(1, 0), KnownZero(1, 0);
+    computeKnownBits(CondVal, KnownZero, KnownOne, Q.DL, 0, Q.AC, Q.CxtI, Q.DT);
+    if (KnownOne == 1)
+      return TrueVal;
+    if (KnownZero == 1)
+      return FalseVal;
+  }
+
   return nullptr;
 }
 
Index: test/Transforms/InstSimplify/select.ll
===================================================================
--- test/Transforms/InstSimplify/select.ll
+++ test/Transforms/InstSimplify/select.ll
@@ -402,15 +402,14 @@
   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.
 
 declare void @llvm.assume(i1)
 
 define i8 @assume_sel_cond(i1 %cond, i8 %x, i8 %y) {
 ; CHECK-LABEL: @assume_sel_cond(
 ; CHECK-NEXT:    call void @llvm.assume(i1 %cond)
-; CHECK-NEXT:    [[SEL:%.*]] = select i1 %cond, i8 %x, i8 %y
-; CHECK-NEXT:    ret i8 [[SEL]]
+; CHECK-NEXT:    ret i8 %x
 ;
   call void @llvm.assume(i1 %cond)
   %sel = select i1 %cond, i8 %x, i8 %y
@@ -421,8 +420,7 @@
 ; CHECK-LABEL: @do_not_assume_sel_cond(
 ; CHECK-NEXT:    [[NOTCOND:%.*]] = icmp eq i1 %cond, false
 ; CHECK-NEXT:    call void @llvm.assume(i1 [[NOTCOND]])
-; CHECK-NEXT:    [[SEL:%.*]] = select i1 %cond, i8 %x, i8 %y
-; CHECK-NEXT:    ret i8 [[SEL]]
+; CHECK-NEXT:    ret i8 %y
 ;
   %notcond = icmp eq i1 %cond, false
   call void @llvm.assume(i1 %notcond)