diff --git a/llvm/lib/Transforms/IPO/AttributorAttributes.cpp b/llvm/lib/Transforms/IPO/AttributorAttributes.cpp
--- a/llvm/lib/Transforms/IPO/AttributorAttributes.cpp
+++ b/llvm/lib/Transforms/IPO/AttributorAttributes.cpp
@@ -265,10 +265,11 @@
         DepClassTy::NONE);
   bool AnyDead = false;
 
+  Value *InitialV = &IRP.getAssociatedValue();
   using Item = std::pair<Value *, const Instruction *>;
   SmallSet<Item, 16> Visited;
   SmallVector<Item, 16> Worklist;
-  Worklist.push_back({&IRP.getAssociatedValue(), CtxI});
+  Worklist.push_back({InitialV, CtxI});
 
   int Iteration = 0;
   do {
@@ -307,8 +308,22 @@
       continue;
     }
 
-    // Look through select instructions, visit both potential values.
+    // Look through select instructions, visit assumed potential values.
     if (auto *SI = dyn_cast<SelectInst>(V)) {
+      bool UsedAssumedInformation = false;
+      Optional<Constant *> C = A.getAssumedConstant(
+          *SI->getCondition(), QueryingAA, UsedAssumedInformation);
+      bool NoValueYet = !C.hasValue();
+      if (NoValueYet || isa_and_nonnull<UndefValue>(*C))
+        continue;
+      if (auto *CI = dyn_cast_or_null<ConstantInt>(*C)) {
+        if (CI->isZero())
+          Worklist.push_back({SI->getFalseValue(), CtxI});
+        else
+          Worklist.push_back({SI->getTrueValue(), CtxI});
+        continue;
+      }
+      // We could not simplify the condition, assume both values.(
       Worklist.push_back({SI->getTrueValue(), CtxI});
       Worklist.push_back({SI->getFalseValue(), CtxI});
       continue;
diff --git a/llvm/test/Transforms/Attributor/lvi-for-ashr.ll b/llvm/test/Transforms/Attributor/lvi-for-ashr.ll
--- a/llvm/test/Transforms/Attributor/lvi-for-ashr.ll
+++ b/llvm/test/Transforms/Attributor/lvi-for-ashr.ll
@@ -7,47 +7,87 @@
 ; FIXME: DOT should be replaced with 3
 
 define i32 @test-ashr(i32 %c) {
-; IS__TUNIT____: Function Attrs: nofree nosync nounwind readnone willreturn
-; IS__TUNIT____-LABEL: define {{[^@]+}}@test-ashr
-; IS__TUNIT____-SAME: (i32 [[C:%.*]]) #[[ATTR0:[0-9]+]] {
-; IS__TUNIT____-NEXT:  chk65:
-; IS__TUNIT____-NEXT:    [[CMP:%.*]] = icmp sgt i32 [[C]], 65
-; IS__TUNIT____-NEXT:    br i1 [[CMP]], label [[RETURN:%.*]], label [[CHK0:%.*]]
-; IS__TUNIT____:       chk0:
-; IS__TUNIT____-NEXT:    [[CMP1:%.*]] = icmp slt i32 [[C]], 0
-; IS__TUNIT____-NEXT:    br i1 [[CMP]], label [[RETURN]], label [[BB_IF:%.*]]
-; IS__TUNIT____:       bb_if:
-; IS__TUNIT____-NEXT:    [[ASHR_VAL:%.*]] = ashr exact i32 [[C]], 2
-; IS__TUNIT____-NEXT:    [[CMP2:%.*]] = icmp sgt i32 [[ASHR_VAL]], 15
-; IS__TUNIT____-NEXT:    br i1 [[CMP2]], label [[BB_THEN:%.*]], label [[RETURN]]
-; IS__TUNIT____:       bb_then:
-; IS__TUNIT____-NEXT:    [[CMP3:%.*]] = icmp eq i32 [[ASHR_VAL]], 16
-; IS__TUNIT____-NEXT:    [[DOT:%.*]] = select i1 [[CMP3]], i32 3, i32 2
-; IS__TUNIT____-NEXT:    br label [[RETURN]]
-; IS__TUNIT____:       return:
-; IS__TUNIT____-NEXT:    [[RETVAL:%.*]] = phi i32 [ 0, [[CHK65:%.*]] ], [ 1, [[CHK0]] ], [ [[DOT]], [[BB_THEN]] ], [ 4, [[BB_IF]] ]
-; IS__TUNIT____-NEXT:    ret i32 [[RETVAL]]
+; IS__TUNIT_OPM: Function Attrs: nofree nosync nounwind readnone willreturn
+; IS__TUNIT_OPM-LABEL: define {{[^@]+}}@test-ashr
+; IS__TUNIT_OPM-SAME: (i32 [[C:%.*]]) #[[ATTR0:[0-9]+]] {
+; IS__TUNIT_OPM-NEXT:  chk65:
+; IS__TUNIT_OPM-NEXT:    [[CMP:%.*]] = icmp sgt i32 [[C]], 65
+; IS__TUNIT_OPM-NEXT:    br i1 [[CMP]], label [[RETURN:%.*]], label [[CHK0:%.*]]
+; IS__TUNIT_OPM:       chk0:
+; IS__TUNIT_OPM-NEXT:    [[CMP1:%.*]] = icmp slt i32 [[C]], 0
+; IS__TUNIT_OPM-NEXT:    br i1 [[CMP]], label [[RETURN]], label [[BB_IF:%.*]]
+; IS__TUNIT_OPM:       bb_if:
+; IS__TUNIT_OPM-NEXT:    [[ASHR_VAL:%.*]] = ashr exact i32 [[C]], 2
+; IS__TUNIT_OPM-NEXT:    [[CMP2:%.*]] = icmp sgt i32 [[ASHR_VAL]], 15
+; IS__TUNIT_OPM-NEXT:    br i1 [[CMP2]], label [[BB_THEN:%.*]], label [[RETURN]]
+; IS__TUNIT_OPM:       bb_then:
+; IS__TUNIT_OPM-NEXT:    [[CMP3:%.*]] = icmp eq i32 [[ASHR_VAL]], 16
+; IS__TUNIT_OPM-NEXT:    [[DOT:%.*]] = select i1 [[CMP3]], i32 3, i32 2
+; IS__TUNIT_OPM-NEXT:    br label [[RETURN]]
+; IS__TUNIT_OPM:       return:
+; IS__TUNIT_OPM-NEXT:    [[RETVAL:%.*]] = phi i32 [ 0, [[CHK65:%.*]] ], [ 1, [[CHK0]] ], [ [[DOT]], [[BB_THEN]] ], [ 4, [[BB_IF]] ]
+; IS__TUNIT_OPM-NEXT:    ret i32 [[RETVAL]]
 ;
-; IS__CGSCC____: Function Attrs: nofree norecurse nosync nounwind readnone willreturn
-; IS__CGSCC____-LABEL: define {{[^@]+}}@test-ashr
-; IS__CGSCC____-SAME: (i32 [[C:%.*]]) #[[ATTR0:[0-9]+]] {
-; IS__CGSCC____-NEXT:  chk65:
-; IS__CGSCC____-NEXT:    [[CMP:%.*]] = icmp sgt i32 [[C]], 65
-; IS__CGSCC____-NEXT:    br i1 [[CMP]], label [[RETURN:%.*]], label [[CHK0:%.*]]
-; IS__CGSCC____:       chk0:
-; IS__CGSCC____-NEXT:    [[CMP1:%.*]] = icmp slt i32 [[C]], 0
-; IS__CGSCC____-NEXT:    br i1 [[CMP]], label [[RETURN]], label [[BB_IF:%.*]]
-; IS__CGSCC____:       bb_if:
-; IS__CGSCC____-NEXT:    [[ASHR_VAL:%.*]] = ashr exact i32 [[C]], 2
-; IS__CGSCC____-NEXT:    [[CMP2:%.*]] = icmp sgt i32 [[ASHR_VAL]], 15
-; IS__CGSCC____-NEXT:    br i1 [[CMP2]], label [[BB_THEN:%.*]], label [[RETURN]]
-; IS__CGSCC____:       bb_then:
-; IS__CGSCC____-NEXT:    [[CMP3:%.*]] = icmp eq i32 [[ASHR_VAL]], 16
-; IS__CGSCC____-NEXT:    [[DOT:%.*]] = select i1 [[CMP3]], i32 3, i32 2
-; IS__CGSCC____-NEXT:    br label [[RETURN]]
-; IS__CGSCC____:       return:
-; IS__CGSCC____-NEXT:    [[RETVAL:%.*]] = phi i32 [ 0, [[CHK65:%.*]] ], [ 1, [[CHK0]] ], [ [[DOT]], [[BB_THEN]] ], [ 4, [[BB_IF]] ]
-; IS__CGSCC____-NEXT:    ret i32 [[RETVAL]]
+; IS__TUNIT_NPM: Function Attrs: nofree nosync nounwind readnone willreturn
+; IS__TUNIT_NPM-LABEL: define {{[^@]+}}@test-ashr
+; IS__TUNIT_NPM-SAME: (i32 [[C:%.*]]) #[[ATTR0:[0-9]+]] {
+; IS__TUNIT_NPM-NEXT:  chk65:
+; IS__TUNIT_NPM-NEXT:    [[CMP:%.*]] = icmp sgt i32 [[C]], 65
+; IS__TUNIT_NPM-NEXT:    br i1 [[CMP]], label [[RETURN:%.*]], label [[CHK0:%.*]]
+; IS__TUNIT_NPM:       chk0:
+; IS__TUNIT_NPM-NEXT:    [[CMP1:%.*]] = icmp slt i32 [[C]], 0
+; IS__TUNIT_NPM-NEXT:    br i1 [[CMP]], label [[RETURN]], label [[BB_IF:%.*]]
+; IS__TUNIT_NPM:       bb_if:
+; IS__TUNIT_NPM-NEXT:    [[ASHR_VAL:%.*]] = ashr exact i32 [[C]], 2
+; IS__TUNIT_NPM-NEXT:    [[CMP2:%.*]] = icmp sgt i32 [[ASHR_VAL]], 15
+; IS__TUNIT_NPM-NEXT:    br i1 [[CMP2]], label [[BB_THEN:%.*]], label [[RETURN]]
+; IS__TUNIT_NPM:       bb_then:
+; IS__TUNIT_NPM-NEXT:    [[DOT:%.*]] = select i1 true, i32 3, i32 2
+; IS__TUNIT_NPM-NEXT:    br label [[RETURN]]
+; IS__TUNIT_NPM:       return:
+; IS__TUNIT_NPM-NEXT:    [[RETVAL:%.*]] = phi i32 [ 0, [[CHK65:%.*]] ], [ 1, [[CHK0]] ], [ [[DOT]], [[BB_THEN]] ], [ 4, [[BB_IF]] ]
+; IS__TUNIT_NPM-NEXT:    ret i32 [[RETVAL]]
+;
+; IS__CGSCC_OPM: Function Attrs: nofree norecurse nosync nounwind readnone willreturn
+; IS__CGSCC_OPM-LABEL: define {{[^@]+}}@test-ashr
+; IS__CGSCC_OPM-SAME: (i32 [[C:%.*]]) #[[ATTR0:[0-9]+]] {
+; IS__CGSCC_OPM-NEXT:  chk65:
+; IS__CGSCC_OPM-NEXT:    [[CMP:%.*]] = icmp sgt i32 [[C]], 65
+; IS__CGSCC_OPM-NEXT:    br i1 [[CMP]], label [[RETURN:%.*]], label [[CHK0:%.*]]
+; IS__CGSCC_OPM:       chk0:
+; IS__CGSCC_OPM-NEXT:    [[CMP1:%.*]] = icmp slt i32 [[C]], 0
+; IS__CGSCC_OPM-NEXT:    br i1 [[CMP]], label [[RETURN]], label [[BB_IF:%.*]]
+; IS__CGSCC_OPM:       bb_if:
+; IS__CGSCC_OPM-NEXT:    [[ASHR_VAL:%.*]] = ashr exact i32 [[C]], 2
+; IS__CGSCC_OPM-NEXT:    [[CMP2:%.*]] = icmp sgt i32 [[ASHR_VAL]], 15
+; IS__CGSCC_OPM-NEXT:    br i1 [[CMP2]], label [[BB_THEN:%.*]], label [[RETURN]]
+; IS__CGSCC_OPM:       bb_then:
+; IS__CGSCC_OPM-NEXT:    [[CMP3:%.*]] = icmp eq i32 [[ASHR_VAL]], 16
+; IS__CGSCC_OPM-NEXT:    [[DOT:%.*]] = select i1 [[CMP3]], i32 3, i32 2
+; IS__CGSCC_OPM-NEXT:    br label [[RETURN]]
+; IS__CGSCC_OPM:       return:
+; IS__CGSCC_OPM-NEXT:    [[RETVAL:%.*]] = phi i32 [ 0, [[CHK65:%.*]] ], [ 1, [[CHK0]] ], [ [[DOT]], [[BB_THEN]] ], [ 4, [[BB_IF]] ]
+; IS__CGSCC_OPM-NEXT:    ret i32 [[RETVAL]]
+;
+; IS__CGSCC_NPM: Function Attrs: nofree norecurse nosync nounwind readnone willreturn
+; IS__CGSCC_NPM-LABEL: define {{[^@]+}}@test-ashr
+; IS__CGSCC_NPM-SAME: (i32 [[C:%.*]]) #[[ATTR0:[0-9]+]] {
+; IS__CGSCC_NPM-NEXT:  chk65:
+; IS__CGSCC_NPM-NEXT:    [[CMP:%.*]] = icmp sgt i32 [[C]], 65
+; IS__CGSCC_NPM-NEXT:    br i1 [[CMP]], label [[RETURN:%.*]], label [[CHK0:%.*]]
+; IS__CGSCC_NPM:       chk0:
+; IS__CGSCC_NPM-NEXT:    [[CMP1:%.*]] = icmp slt i32 [[C]], 0
+; IS__CGSCC_NPM-NEXT:    br i1 [[CMP]], label [[RETURN]], label [[BB_IF:%.*]]
+; IS__CGSCC_NPM:       bb_if:
+; IS__CGSCC_NPM-NEXT:    [[ASHR_VAL:%.*]] = ashr exact i32 [[C]], 2
+; IS__CGSCC_NPM-NEXT:    [[CMP2:%.*]] = icmp sgt i32 [[ASHR_VAL]], 15
+; IS__CGSCC_NPM-NEXT:    br i1 [[CMP2]], label [[BB_THEN:%.*]], label [[RETURN]]
+; IS__CGSCC_NPM:       bb_then:
+; IS__CGSCC_NPM-NEXT:    [[DOT:%.*]] = select i1 true, i32 3, i32 2
+; IS__CGSCC_NPM-NEXT:    br label [[RETURN]]
+; IS__CGSCC_NPM:       return:
+; IS__CGSCC_NPM-NEXT:    [[RETVAL:%.*]] = phi i32 [ 0, [[CHK65:%.*]] ], [ 1, [[CHK0]] ], [ [[DOT]], [[BB_THEN]] ], [ 4, [[BB_IF]] ]
+; IS__CGSCC_NPM-NEXT:    ret i32 [[RETVAL]]
 ;
 chk65:
   %cmp = icmp sgt i32 %c, 65
@@ -72,7 +112,7 @@
   ret i32 %retval
 }
 ;.
-; IS__TUNIT____: attributes #[[ATTR0]] = { nofree nosync nounwind readnone willreturn }
+; IS__TUNIT____: attributes #[[ATTR0:[0-9]+]] = { nofree nosync nounwind readnone willreturn }
 ;.
-; IS__CGSCC____: attributes #[[ATTR0]] = { nofree norecurse nosync nounwind readnone willreturn }
+; IS__CGSCC____: attributes #[[ATTR0:[0-9]+]] = { nofree norecurse nosync nounwind readnone willreturn }
 ;.
diff --git a/llvm/test/Transforms/Attributor/value-simplify.ll b/llvm/test/Transforms/Attributor/value-simplify.ll
--- a/llvm/test/Transforms/Attributor/value-simplify.ll
+++ b/llvm/test/Transforms/Attributor/value-simplify.ll
@@ -1039,8 +1039,7 @@
 ; IS__TUNIT____: Function Attrs: nofree nosync nounwind readnone willreturn
 ; IS__TUNIT____-LABEL: define {{[^@]+}}@test_select
 ; IS__TUNIT____-SAME: (i32 [[C:%.*]]) #[[ATTR1]] {
-; IS__TUNIT____-NEXT:    [[CALL:%.*]] = call i32 @select() #[[ATTR1]]
-; IS__TUNIT____-NEXT:    ret i32 [[CALL]]
+; IS__TUNIT____-NEXT:    ret i32 42
 ;
 ; IS__CGSCC____: Function Attrs: nofree norecurse nosync nounwind readnone willreturn
 ; IS__CGSCC____-LABEL: define {{[^@]+}}@test_select
@@ -1052,11 +1051,6 @@
 }
 
 define internal i32 @select(i1 %a, i32 %b, i32 %c) {
-; IS__TUNIT____: Function Attrs: nofree nosync nounwind readnone willreturn
-; IS__TUNIT____-LABEL: define {{[^@]+}}@select
-; IS__TUNIT____-SAME: () #[[ATTR1]] {
-; IS__TUNIT____-NEXT:    ret i32 42
-;
 ; IS__CGSCC____: Function Attrs: nofree norecurse nosync nounwind readnone willreturn
 ; IS__CGSCC____-LABEL: define {{[^@]+}}@select
 ; IS__CGSCC____-SAME: () #[[ATTR1]] {