diff --git a/llvm/lib/Transforms/InstCombine/InstCombineAndOrXor.cpp b/llvm/lib/Transforms/InstCombine/InstCombineAndOrXor.cpp
--- a/llvm/lib/Transforms/InstCombine/InstCombineAndOrXor.cpp
+++ b/llvm/lib/Transforms/InstCombine/InstCombineAndOrXor.cpp
@@ -2251,8 +2251,19 @@
     case ICmpInst::ICMP_EQ:
       // Potential folds for this case should already be handled.
       break;
-    case ICmpInst::ICMP_UGT: // (X == 13 | X u> 14) -> no change
-    case ICmpInst::ICMP_SGT: // (X == 13 | X s> 14) -> no change
+    case ICmpInst::ICMP_UGT:
+      // We can treat equality of MIN_UINT as being ULE MIN_UINT.
+      if (LHSC->isMinValue(false))
+        return insertRangeTest(LHS0, LHSC->getValue() + 1, RHSC->getValue() + 1,
+                               false, false);
+      // (X == 13 | X u> 14) -> no change
+      break;
+    case ICmpInst::ICMP_SGT:
+      // We can treat equality of MIN_SINT as being ULE MIN_SINT.
+      if (LHSC->isMinValue(true))
+        return insertRangeTest(LHS0, LHSC->getValue() + 1, RHSC->getValue() + 1,
+                               true, false);
+      // (X == 13 | X s> 14) -> no change
       break;
     }
     break;
@@ -2261,6 +2272,10 @@
     default:
       llvm_unreachable("Unknown integer condition code!");
     case ICmpInst::ICMP_EQ: // (X u< 13 | X == 14) -> no change
+      // We can treat equality of MAX_UINT as being UGE MAX_UINT.
+      if (RHSC->isMaxValue(false))
+        return insertRangeTest(LHS0, LHSC->getValue(), RHSC->getValue(),
+                               false, false);
       break;
     case ICmpInst::ICMP_UGT: // (X u< 13 | X u> 15) -> (X-13) u> 2
       assert(!RHSC->isMaxValue(false) && "Missed icmp simplification");
@@ -2272,7 +2287,12 @@
     switch (PredR) {
     default:
       llvm_unreachable("Unknown integer condition code!");
-    case ICmpInst::ICMP_EQ: // (X s< 13 | X == 14) -> no change
+    case ICmpInst::ICMP_EQ:
+      // We can treat equality of MAX_SINT as being SGE MAX_SINT.
+      if (RHSC->isMaxValue(true))
+        return insertRangeTest(LHS0, LHSC->getValue(), RHSC->getValue(),
+                               true, false);
+      // (X s< 13 | X == 14) -> no change
       break;
     case ICmpInst::ICMP_SGT: // (X s< 13 | X s> 15) -> (X-13) s> 2
       assert(!RHSC->isMaxValue(true) && "Missed icmp simplification");
diff --git a/llvm/test/Transforms/InstCombine/and-or-icmps.ll b/llvm/test/Transforms/InstCombine/and-or-icmps.ll
--- a/llvm/test/Transforms/InstCombine/and-or-icmps.ll
+++ b/llvm/test/Transforms/InstCombine/and-or-icmps.ll
@@ -255,10 +255,8 @@
 
 define i1 @PR42691_1(i32 %x) {
 ; CHECK-LABEL: @PR42691_1(
-; CHECK-NEXT:    [[C1:%.*]] = icmp slt i32 %x, 0
-; CHECK-NEXT:    [[C2:%.*]] = icmp eq i32 %x, 2147483647
-; CHECK-NEXT:    [[C:%.*]] = or i1 [[C1]], [[C2]]
-; CHECK-NEXT:    ret i1 [[C]]
+; CHECK-NEXT:    [[TMP1:%.*]] = icmp ugt i32 %x, 2147483646
+; CHECK-NEXT:    ret i1 [[TMP1]]
 ;
   %c1 = icmp slt i32 %x, 0
   %c2 = icmp eq i32 %x, 2147483647
@@ -279,10 +277,8 @@
 
 define i1 @PR42691_3(i32 %x) {
 ; CHECK-LABEL: @PR42691_3(
-; CHECK-NEXT:    [[C1:%.*]] = icmp sgt i32 %x, -1
-; CHECK-NEXT:    [[C2:%.*]] = icmp eq i32 %x, -2147483648
-; CHECK-NEXT:    [[C:%.*]] = or i1 [[C1]], [[C2]]
-; CHECK-NEXT:    ret i1 [[C]]
+; CHECK-NEXT:    [[TMP1:%.*]] = icmp ult i32 %x, -2147483647
+; CHECK-NEXT:    ret i1 [[TMP1]]
 ;
   %c1 = icmp sge i32 %x, 0
   %c2 = icmp eq i32 %x, -2147483648
@@ -303,10 +299,9 @@
 
 define i1 @PR42691_5(i32 %x) {
 ; CHECK-LABEL: @PR42691_5(
-; CHECK-NEXT:    [[C1:%.*]] = icmp slt i32 %x, 1
-; CHECK-NEXT:    [[C2:%.*]] = icmp eq i32 %x, 2147483647
-; CHECK-NEXT:    [[C:%.*]] = or i1 [[C1]], [[C2]]
-; CHECK-NEXT:    ret i1 [[C]]
+; CHECK-NEXT:    [[X_OFF:%.*]] = add i32 %x, -1
+; CHECK-NEXT:    [[TMP1:%.*]] = icmp ugt i32 [[X_OFF]], 2147483645
+; CHECK-NEXT:    ret i1 [[TMP1]]
 ;
   %c1 = icmp slt i32 %x, 1
   %c2 = icmp eq i32 %x, 2147483647