diff --git a/llvm/lib/Transforms/Scalar/SCCP.cpp b/llvm/lib/Transforms/Scalar/SCCP.cpp
index 6d674f447da7..35538338c2d8 100644
--- a/llvm/lib/Transforms/Scalar/SCCP.cpp
+++ b/llvm/lib/Transforms/Scalar/SCCP.cpp
@@ -1902,13 +1902,17 @@ bool llvm::runIPSCCP(Module &M, const DataLayout &DL,
 
   // Solve for constants.
   bool ResolvedUndefs = true;
+  Solver.Solve();
   while (ResolvedUndefs) {
-    Solver.Solve();
-
     LLVM_DEBUG(dbgs() << "RESOLVING UNDEFS\n");
     ResolvedUndefs = false;
     for (Function &F : M)
-      ResolvedUndefs |= Solver.ResolvedUndefsIn(F);
+      if (Solver.ResolvedUndefsIn(F)) {
+        // We run Solve() after we resolved an undef in a function, because
+        // we might deduce a fact that eliminates an undef in another function.
+        Solver.Solve();
+        ResolvedUndefs = true;
+      }
   }
 
   bool MadeChanges = false;
diff --git a/llvm/test/Transforms/IPConstantProp/solve-after-each-resolving-undefs-for-function.ll b/llvm/test/Transforms/IPConstantProp/solve-after-each-resolving-undefs-for-function.ll
new file mode 100644
index 000000000000..5e7c323641d3
--- /dev/null
+++ b/llvm/test/Transforms/IPConstantProp/solve-after-each-resolving-undefs-for-function.ll
@@ -0,0 +1,43 @@
+; RUN: opt < %s -ipsccp -S | FileCheck %s
+
+; CHECK-LABEL: @testf(
+; CHECK:         ret i32 undef
+;
+define internal i32 @testf() {
+entry:
+  br i1 undef, label %if.then, label %if.end
+
+if.then:                                          ; preds = %entry, %if.then
+  br label %if.end
+
+if.end:                                          ; preds = %if.then1, %entry
+  ret i32 10
+}
+
+; CHECK-LABEL: @test1(
+; CHECK:         ret i32 undef
+;
+define internal i32 @test1() {
+entry:
+  br label %if.then
+
+if.then:                                          ; preds = %entry, %if.then
+  %call = call i32 @testf()
+  %res = icmp eq i32 %call, 10
+  br i1 %res, label %ret1, label %ret2
+
+ret1:                                           ; preds = %if.then, %entry
+  ret i32 99
+
+ret2:                                           ; preds = %if.then, %entry
+  ret i32 0
+}
+
+; CHECK-LABEL: @main(
+; CHECK-NEXT:    %res = call i32 @test1()
+; CHECK-NEXT:    ret i32 99
+;
+define i32 @main() {
+  %res = call i32 @test1()
+  ret i32 %res
+}
diff --git a/llvm/test/Transforms/SCCP/ipsccp-basic.ll b/llvm/test/Transforms/SCCP/ipsccp-basic.ll
index b7db86891151..ae08b4823c94 100644
--- a/llvm/test/Transforms/SCCP/ipsccp-basic.ll
+++ b/llvm/test/Transforms/SCCP/ipsccp-basic.ll
@@ -247,13 +247,14 @@ define i64 @test11a() {
 ; CHECK: ret i64 0
 }
 
-define void @test11b() {
+define i64 @test11b() {
   %call1 = call i64 @test11a()
   %call2 = call i64 @llvm.ctpop.i64(i64 %call1)
-  ret void
-; CHECK-LABEL: define void @test11b
+  ret i64 %call2
+; CHECK-LABEL: define i64 @test11b
 ; CHECK: %[[call1:.*]] = call i64 @test11a()
-; CHECK: %[[call2:.*]] = call i64 @llvm.ctpop.i64(i64 0)
+; CHECK-NOT: call i64 @llvm.ctpop.i64
+; CHECK-NEXT: ret i64 0
 }
 
 declare i64 @llvm.ctpop.i64(i64)