diff --git a/llvm/lib/Analysis/InstructionSimplify.cpp b/llvm/lib/Analysis/InstructionSimplify.cpp
--- a/llvm/lib/Analysis/InstructionSimplify.cpp
+++ b/llvm/lib/Analysis/InstructionSimplify.cpp
@@ -516,6 +516,63 @@
   return nullptr;
 }
 
+/// In the case of a comparison with two select instructions having the same
+/// condition, try to simplify the comparison by seeing whether all
+/// combinations of branches of the select result in the same value. Returns
+/// the common value if so, otherwise returns null.
+/// For example, if we have:
+///  %tmp1 = select i1 %cmp, i32 1, i32 %param
+///  %tmp2 = select i1 %cmp, i32 9, i32 %param
+///  %cmp2 = icmp slt i32 %tmp2, %tmp1
+/// We can simplify %cmp2 to false, because for both branches of both the
+/// selects will result false.
+static Value *threadCmpOverMultSelect(CmpInst::Predicate Pred, Value *LHS,
+                                      Value *RHS, const SimplifyQuery &Q,
+                                      unsigned MaxRecurse) {
+  // Recursion is always used, so bail out at once if we already hit the limit.
+  if (!MaxRecurse--)
+    return nullptr;
+
+  // Make sure both LHS and RHS are select.
+  assert(isa<SelectInst>(LHS) && isa<SelectInst>(RHS) &&
+         "Not comparing with select instructions!");
+  SelectInst *LHSSI = cast<SelectInst>(LHS);
+  SelectInst *RHSSI = cast<SelectInst>(RHS);
+  Value *LHSCond = LHSSI->getCondition();
+  Value *RHSCond = RHSSI->getCondition();
+  Value *LHSTV = LHSSI->getTrueValue();
+  Value *LHSFV = LHSSI->getFalseValue();
+  Value *RHSTV = RHSSI->getTrueValue();
+  Value *RHSFV = RHSSI->getFalseValue();
+
+  // Make sure that both select have same condition for comparing equivalent
+  // branch.
+  if (LHSCond != RHSCond)
+    return nullptr;
+
+  // Now that we have "cmp select(Cond, LHSTV, LHSFV),
+  //                       select(Cond, RHSTV, RHSFV)",
+  // analyse it.
+  // Does "cmp LHSTV, RHSTV" simplify?
+  Value *TCmp =
+      simplifyCmpSelTrueCase(Pred, LHSTV, RHSTV, LHSCond, Q, MaxRecurse);
+  if (!TCmp)
+    return nullptr;
+
+  // Does "cmp LHSFV, RHSFV" simplify?
+  Value *FCmp =
+      simplifyCmpSelFalseCase(Pred, LHSFV, RHSFV, LHSCond, Q, MaxRecurse);
+  if (!FCmp)
+    return nullptr;
+
+  // If both sides simplified to the same value, then use it as the result of
+  // the original comparison.
+  if (TCmp == FCmp)
+    return TCmp;
+
+  return nullptr;
+}
+
 /// In the case of a binary operation with an operand that is a PHI instruction,
 /// try to simplify the binop by seeing whether evaluating it on the incoming
 /// phi values yields the same result for every value. If so returns the common
@@ -3964,6 +4021,13 @@
     if (Value *V = threadCmpOverSelect(Pred, LHS, RHS, Q, MaxRecurse))
       return V;
 
+  // If the comparison is with the result of two select instructions with the
+  // same condition, check whether comparing with the equivalent branches of
+  // the selects always yields the same value.
+  if (isa<SelectInst>(LHS) && isa<SelectInst>(RHS))
+    if (Value *V = threadCmpOverMultSelect(Pred, LHS, RHS, Q, MaxRecurse))
+      return V;
+
   // If the comparison is with the result of a phi instruction, check whether
   // doing the compare with each incoming phi value yields a common result.
   if (isa<PHINode>(LHS) || isa<PHINode>(RHS))
diff --git a/llvm/test/Transforms/InstSimplify/icmp-with-selects.ll b/llvm/test/Transforms/InstSimplify/icmp-with-selects.ll
new file mode 100644
--- /dev/null
+++ b/llvm/test/Transforms/InstSimplify/icmp-with-selects.ll
@@ -0,0 +1,31 @@
+; NOTE: Assertions have been autogenerated by utils/update_test_checks.py UTC_ARGS: --version 2
+; RUN: opt < %s -passes=instsimplify -S | FileCheck %s
+
+define i32 @_Z3fooib(i32 noundef %param, i1 noundef zeroext %cond) {
+; CHECK-LABEL: define i32 @_Z3fooib
+; CHECK-SAME: (i32 noundef [[PARAM:%.*]], i1 noundef zeroext [[COND:%.*]]) {
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    ret i32 0
+;
+entry:
+  %cond1 = select i1 %cond, i32 1, i32 %param
+  %cond6 = select i1 %cond, i32 9, i32 %param
+  %cmp = icmp slt i32 %cond6, %cond1
+  %cond7 = zext i1 %cmp to i32
+  ret i32 %cond7
+}
+
+define i32 @_Z3barib(i32 noundef %param, i1 noundef zeroext %cond) {
+; CHECK-LABEL: define i32 @_Z3barib
+; CHECK-SAME: (i32 noundef [[PARAM:%.*]], i1 noundef zeroext [[COND:%.*]]) {
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    ret i32 0
+;
+entry:
+  %cond1 = select i1 %cond, i32 9, i32 %param
+  %cond6 = select i1 %cond, i32 1, i32 %param
+  %cmp = icmp sgt i32 %cond6, %cond1
+  %cond7 = zext i1 %cmp to i32
+  ret i32 %cond7
+}
+