diff --git a/llvm/lib/Transforms/Scalar/SCCP.cpp b/llvm/lib/Transforms/Scalar/SCCP.cpp
--- a/llvm/lib/Transforms/Scalar/SCCP.cpp
+++ b/llvm/lib/Transforms/Scalar/SCCP.cpp
@@ -1004,6 +1004,21 @@
     if (isConstant(V1State) && getConstant(V1State)->isNullValue())
       return (void)markConstant(IV, &I, getConstant(V1State));
 
+  // ANDs restricts the range of the result, if either operand is a constant
+  // range.
+  if (I.getOpcode() == Instruction::And &&
+      (V1State.isConstantRange() || V2State.isConstantRange())) {
+    auto A = V1State.isConstantRange()
+                 ? V1State.getConstantRange()
+                 : ConstantRange::getFull(I.getType()->getScalarSizeInBits());
+    auto B = V2State.isConstantRange()
+                 ? V2State.getConstantRange()
+                 : ConstantRange::getFull(I.getType()->getScalarSizeInBits());
+    ConstantRange R = A.binaryOp(cast<BinaryOperator>(&I)->getOpcode(), B);
+    mergeInValue(&I, LatticeVal::getRange(R));
+    return;
+  }
+
   // If this is:
   // -> AND/MUL with 0
   // -> OR with -1
diff --git a/llvm/test/Transforms/SCCP/range-and.ll b/llvm/test/Transforms/SCCP/range-and.ll
new file mode 100644
--- /dev/null
+++ b/llvm/test/Transforms/SCCP/range-and.ll
@@ -0,0 +1,240 @@
+; NOTE: Assertions have been autogenerated by utils/update_test_checks.py
+; RUN: opt -S -sccp %s | FileCheck %s
+
+; Test case for PR44949.
+
+; We can remove `%res = and i64 %p, 255`, because %r = 0 and we can eliminate
+; %p as well.
+define i64 @constant_and_undef(i1 %c1, i64 %a) {
+; CHECK-LABEL: @constant_and_undef(
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    br i1 [[C1:%.*]], label [[BB1:%.*]], label [[BB2:%.*]]
+; CHECK:       bb1:
+; CHECK-NEXT:    br label [[BB3:%.*]]
+; CHECK:       bb2:
+; CHECK-NEXT:    br label [[BB3]]
+; CHECK:       bb3:
+; CHECK-NEXT:    ret i64 0
+;
+entry:
+  br i1 %c1, label %bb1, label %bb2
+
+bb1:
+  br label %bb3
+
+bb2:
+  %r = and i64 %a, 0
+  br label %bb3
+
+bb3:
+  %p = phi i64 [ undef, %bb1 ], [ %r, %bb2 ]
+  %res = and i64 %p, 255
+  ret i64 %res
+}
+
+; Check that we go to overdefined when merging a constant range with undef. We
+; cannot remove '%res = and i64 %p, 255'.
+define i64 @constant_range_and_undef(i1 %cond, i64 %a) {
+; CHECK-LABEL: @constant_range_and_undef(
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    br i1 [[COND:%.*]], label [[BB1:%.*]], label [[BB2:%.*]]
+; CHECK:       bb1:
+; CHECK-NEXT:    br label [[BB3:%.*]]
+; CHECK:       bb2:
+; CHECK-NEXT:    [[R:%.*]] = and i64 [[A:%.*]], 255
+; CHECK-NEXT:    br label [[BB3]]
+; CHECK:       bb3:
+; CHECK-NEXT:    [[P:%.*]] = phi i64 [ undef, [[BB1]] ], [ [[R]], [[BB2]] ]
+; CHECK-NEXT:    [[RES:%.*]] = and i64 [[P]], 255
+; CHECK-NEXT:    ret i64 [[RES]]
+;
+entry:
+  br i1 %cond, label %bb1, label %bb2
+
+bb1:
+  br label %bb3
+
+bb2:
+  %r = and i64 %a, 255
+  br label %bb3
+
+bb3:
+  %p = phi i64 [ undef, %bb1 ], [ %r, %bb2 ]
+  %res = and i64 %p, 255
+  ret i64 %res
+}
+
+; Same as @constant_range_and_undef, with the undef coming from the other
+; block.
+define i64 @constant_range_and_undef_switched_incoming(i1 %cond, i64 %a) {
+; CHECK-LABEL: @constant_range_and_undef_switched_incoming(
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    br i1 [[COND:%.*]], label [[BB1:%.*]], label [[BB2:%.*]]
+; CHECK:       bb1:
+; CHECK-NEXT:    [[R:%.*]] = and i64 [[A:%.*]], 255
+; CHECK-NEXT:    br label [[BB3:%.*]]
+; CHECK:       bb2:
+; CHECK-NEXT:    br label [[BB3]]
+; CHECK:       bb3:
+; CHECK-NEXT:    [[P:%.*]] = phi i64 [ [[R]], [[BB1]] ], [ undef, [[BB2]] ]
+; CHECK-NEXT:    [[RES:%.*]] = and i64 [[P]], 255
+; CHECK-NEXT:    ret i64 [[RES]]
+;
+entry:
+  br i1 %cond, label %bb1, label %bb2
+
+bb1:
+  %r = and i64 %a, 255
+  br label %bb3
+
+bb2:
+  br label %bb3
+
+bb3:
+  %p = phi i64 [ %r, %bb1 ], [ undef, %bb2 ]
+  %res = and i64 %p, 255
+  ret i64 %res
+}
+
+define i1 @constant_range_and_255_100(i1 %cond, i64 %a) {
+; CHECK-LABEL: @constant_range_and_255_100(
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    br i1 [[COND:%.*]], label [[BB1:%.*]], label [[BB2:%.*]]
+; CHECK:       bb1:
+; CHECK-NEXT:    [[R_1:%.*]] = and i64 [[A:%.*]], 100
+; CHECK-NEXT:    br label [[BB3:%.*]]
+; CHECK:       bb2:
+; CHECK-NEXT:    [[R_2:%.*]] = and i64 [[A]], 255
+; CHECK-NEXT:    br label [[BB3]]
+; CHECK:       bb3:
+; CHECK-NEXT:    [[P:%.*]] = phi i64 [ [[R_1]], [[BB1]] ], [ [[R_2]], [[BB2]] ]
+; CHECK-NEXT:    [[P_AND:%.*]] = and i64 [[P]], 512
+; CHECK-NEXT:    ret i1 true
+;
+entry:
+  br i1 %cond, label %bb1, label %bb2
+
+bb1:
+  %r.1 = and i64 %a, 100
+  br label %bb3
+
+bb2:
+  %r.2 = and i64 %a, 255
+  br label %bb3
+
+bb3:
+  %p = phi i64 [ %r.1, %bb1 ], [ %r.2, %bb2 ]
+  %p.and = and i64 %p, 512
+  %c = icmp ult i64 %p.and, 256
+  ret i1 %c
+}
+
+
+define i64 @constant_range_and_undef2(i1 %c1, i1 %c2, i64 %a) {
+; CHECK-LABEL: @constant_range_and_undef2(
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    br i1 [[C1:%.*]], label [[BB1:%.*]], label [[BB2:%.*]]
+; CHECK:       bb1:
+; CHECK-NEXT:    [[V1:%.*]] = add i64 undef, undef
+; CHECK-NEXT:    br label [[BB3:%.*]]
+; CHECK:       bb2:
+; CHECK-NEXT:    [[V2:%.*]] = and i64 [[A:%.*]], 255
+; CHECK-NEXT:    br label [[BB3]]
+; CHECK:       bb3:
+; CHECK-NEXT:    [[P:%.*]] = phi i64 [ [[V1]], [[BB1]] ], [ [[V2]], [[BB2]] ]
+; CHECK-NEXT:    br i1 [[C2:%.*]], label [[BB4:%.*]], label [[BB5:%.*]]
+; CHECK:       bb4:
+; CHECK-NEXT:    br label [[BB6:%.*]]
+; CHECK:       bb5:
+; CHECK-NEXT:    [[V3:%.*]] = and i64 [[A]], 255
+; CHECK-NEXT:    br label [[BB6]]
+; CHECK:       bb6:
+; CHECK-NEXT:    [[P2:%.*]] = phi i64 [ [[P]], [[BB4]] ], [ [[V3]], [[BB5]] ]
+; CHECK-NEXT:    [[RES:%.*]] = and i64 [[P2]], 255
+; CHECK-NEXT:    ret i64 [[RES]]
+;
+entry:
+  br i1 %c1, label %bb1, label %bb2
+
+bb1:
+  %v1 = add i64 undef, undef
+  br label %bb3
+
+bb2:
+  %v2 = and i64 %a, 255
+  br label %bb3
+
+bb3:
+  %p = phi i64 [ %v1, %bb1 ], [ %v2, %bb2 ]
+  br i1 %c2, label %bb4, label %bb5
+
+bb4:
+  br label %bb6
+
+bb5:
+  %v3 = and i64 %a, 255
+  br label %bb6
+
+bb6:
+  %p2 = phi i64 [ %p, %bb4 ], [ %v3, %bb5 ]
+  %res = and i64 %p2, 255
+  ret i64 %res
+}
+
+define i1 @constant_range_and_undef_3(i1 %cond, i64 %a) {
+; CHECK-LABEL: @constant_range_and_undef_3(
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    br i1 [[COND:%.*]], label [[BB1:%.*]], label [[BB2:%.*]]
+; CHECK:       bb1:
+; CHECK-NEXT:    br label [[BB3:%.*]]
+; CHECK:       bb2:
+; CHECK-NEXT:    [[R:%.*]] = and i64 [[A:%.*]], 255
+; CHECK-NEXT:    br label [[BB3]]
+; CHECK:       bb3:
+; CHECK-NEXT:    [[P:%.*]] = phi i64 [ undef, [[BB1]] ], [ [[R]], [[BB2]] ]
+; CHECK-NEXT:    ret i1 true
+;
+entry:
+  br i1 %cond, label %bb1, label %bb2
+
+bb1:
+  br label %bb3
+
+bb2:
+  %r = and i64 %a, 255
+  br label %bb3
+
+bb3:
+  %p = phi i64 [ undef, %bb1 ], [ %r, %bb2 ]
+  %c = icmp ult i64 %p, 256
+  ret i1 %c
+}
+
+define i1 @constant_range_and_undef_3_switched_incoming(i1 %cond, i64 %a) {
+; CHECK-LABEL: @constant_range_and_undef_3_switched_incoming(
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    br i1 [[COND:%.*]], label [[BB1:%.*]], label [[BB2:%.*]]
+; CHECK:       bb1:
+; CHECK-NEXT:    [[R:%.*]] = and i64 [[A:%.*]], 255
+; CHECK-NEXT:    br label [[BB3:%.*]]
+; CHECK:       bb2:
+; CHECK-NEXT:    br label [[BB3]]
+; CHECK:       bb3:
+; CHECK-NEXT:    [[P:%.*]] = phi i64 [ [[R]], [[BB1]] ], [ undef, [[BB2]] ]
+; CHECK-NEXT:    ret i1 true
+;
+entry:
+  br i1 %cond, label %bb1, label %bb2
+
+bb1:
+  %r = and i64 %a, 255
+  br label %bb3
+
+bb2:
+  br label %bb3
+
+bb3:
+  %p = phi i64 [ %r, %bb1 ], [ undef, %bb2 ]
+  %c = icmp ult i64 %p, 256
+  ret i1 %c
+}