diff --git a/llvm/lib/Transforms/InstCombine/InstCombineSimplifyDemanded.cpp b/llvm/lib/Transforms/InstCombine/InstCombineSimplifyDemanded.cpp
--- a/llvm/lib/Transforms/InstCombine/InstCombineSimplifyDemanded.cpp
+++ b/llvm/lib/Transforms/InstCombine/InstCombineSimplifyDemanded.cpp
@@ -385,8 +385,26 @@
     Known = KnownBits::commonBits(LHSKnown, RHSKnown);
     break;
   }
-  case Instruction::ZExt:
   case Instruction::Trunc: {
+    // If we do not demand the high bits of a right-shifted and truncated value,
+    // then we may be able to truncate it before the shift.
+    Value *X;
+    const APInt *C;
+    if (match(I->getOperand(0), m_OneUse(m_LShr(m_Value(X), m_APInt(C))))) {
+      // The shift amount must be valid (not poison) in the narrow type, and
+      // it must not be greater than the high bits demanded of the result.
+      if (C->ult(I->getType()->getScalarSizeInBits()) &&
+          C->ule(DemandedMask.countLeadingZeros())) {
+        // trunc (lshr X, C) --> lshr (trunc X), C
+        IRBuilderBase::InsertPointGuard Guard(Builder);
+        Builder.SetInsertPoint(I);
+        Value *Trunc = Builder.CreateTrunc(X, I->getType());
+        return Builder.CreateLShr(Trunc, C->getZExtValue());
+      }
+    }
+  }
+    LLVM_FALLTHROUGH;
+  case Instruction::ZExt: {
     unsigned SrcBitWidth = I->getOperand(0)->getType()->getScalarSizeInBits();
 
     APInt InputDemandedMask = DemandedMask.zextOrTrunc(SrcBitWidth);
diff --git a/llvm/test/Transforms/InstCombine/trunc-demand.ll b/llvm/test/Transforms/InstCombine/trunc-demand.ll
--- a/llvm/test/Transforms/InstCombine/trunc-demand.ll
+++ b/llvm/test/Transforms/InstCombine/trunc-demand.ll
@@ -6,9 +6,9 @@
 
 define i6 @trunc_lshr(i8 %x) {
 ; CHECK-LABEL: @trunc_lshr(
-; CHECK-NEXT:    [[S:%.*]] = lshr i8 [[X:%.*]], 2
-; CHECK-NEXT:    [[T:%.*]] = trunc i8 [[S]] to i6
-; CHECK-NEXT:    [[R:%.*]] = and i6 [[T]], 14
+; CHECK-NEXT:    [[TMP1:%.*]] = trunc i8 [[X:%.*]] to i6
+; CHECK-NEXT:    [[TMP2:%.*]] = lshr i6 [[TMP1]], 2
+; CHECK-NEXT:    [[R:%.*]] = and i6 [[TMP2]], 14
 ; CHECK-NEXT:    ret i6 [[R]]
 ;
   %s = lshr i8 %x, 2
@@ -17,12 +17,13 @@
   ret i6 %r
 }
 
+; The 'and' is eliminated.
+
 define i6 @trunc_lshr_exact_mask(i8 %x) {
 ; CHECK-LABEL: @trunc_lshr_exact_mask(
-; CHECK-NEXT:    [[S:%.*]] = lshr i8 [[X:%.*]], 2
-; CHECK-NEXT:    [[T:%.*]] = trunc i8 [[S]] to i6
-; CHECK-NEXT:    [[R:%.*]] = and i6 [[T]], 15
-; CHECK-NEXT:    ret i6 [[R]]
+; CHECK-NEXT:    [[TMP1:%.*]] = trunc i8 [[X:%.*]] to i6
+; CHECK-NEXT:    [[TMP2:%.*]] = lshr i6 [[TMP1]], 2
+; CHECK-NEXT:    ret i6 [[TMP2]]
 ;
   %s = lshr i8 %x, 2
   %t = trunc i8 %s to i6
@@ -30,6 +31,8 @@
   ret i6 %r
 }
 
+; negative test - a high bit of x is in the result
+
 define i6 @trunc_lshr_big_mask(i8 %x) {
 ; CHECK-LABEL: @trunc_lshr_big_mask(
 ; CHECK-NEXT:    [[S:%.*]] = lshr i8 [[X:%.*]], 2
@@ -43,6 +46,8 @@
   ret i6 %r
 }
 
+; negative test - too many uses
+
 define i6 @trunc_lshr_use1(i8 %x) {
 ; CHECK-LABEL: @trunc_lshr_use1(
 ; CHECK-NEXT:    [[S:%.*]] = lshr i8 [[X:%.*]], 2
@@ -58,6 +63,8 @@
   ret i6 %r
 }
 
+; negative test - too many uses
+
 define i6 @trunc_lshr_use2(i8 %x) {
 ; CHECK-LABEL: @trunc_lshr_use2(
 ; CHECK-NEXT:    [[S:%.*]] = lshr i8 [[X:%.*]], 2
@@ -73,11 +80,13 @@
   ret i6 %r
 }
 
+; Splat vectors are ok.
+
 define <2 x i7> @trunc_lshr_vec_splat(<2 x i16> %x) {
 ; CHECK-LABEL: @trunc_lshr_vec_splat(
-; CHECK-NEXT:    [[S:%.*]] = lshr <2 x i16> [[X:%.*]], <i16 5, i16 5>
-; CHECK-NEXT:    [[T:%.*]] = trunc <2 x i16> [[S]] to <2 x i7>
-; CHECK-NEXT:    [[R:%.*]] = and <2 x i7> [[T]], <i7 1, i7 1>
+; CHECK-NEXT:    [[TMP1:%.*]] = trunc <2 x i16> [[X:%.*]] to <2 x i7>
+; CHECK-NEXT:    [[TMP2:%.*]] = lshr <2 x i7> [[TMP1]], <i7 5, i7 5>
+; CHECK-NEXT:    [[R:%.*]] = and <2 x i7> [[TMP2]], <i7 1, i7 1>
 ; CHECK-NEXT:    ret <2 x i7> [[R]]
 ;
   %s = lshr <2 x i16> %x, <i16 5, i16 5>
@@ -86,12 +95,13 @@
   ret <2 x i7> %r
 }
 
+; The 'and' is eliminated.
+
 define <2 x i7> @trunc_lshr_vec_splat_exact_mask(<2 x i16> %x) {
 ; CHECK-LABEL: @trunc_lshr_vec_splat_exact_mask(
-; CHECK-NEXT:    [[S:%.*]] = lshr <2 x i16> [[X:%.*]], <i16 6, i16 6>
-; CHECK-NEXT:    [[T:%.*]] = trunc <2 x i16> [[S]] to <2 x i7>
-; CHECK-NEXT:    [[R:%.*]] = and <2 x i7> [[T]], <i7 1, i7 1>
-; CHECK-NEXT:    ret <2 x i7> [[R]]
+; CHECK-NEXT:    [[TMP1:%.*]] = trunc <2 x i16> [[X:%.*]] to <2 x i7>
+; CHECK-NEXT:    [[TMP2:%.*]] = lshr <2 x i7> [[TMP1]], <i7 6, i7 6>
+; CHECK-NEXT:    ret <2 x i7> [[TMP2]]
 ;
   %s = lshr <2 x i16> %x, <i16 6, i16 6>
   %t = trunc <2 x i16> %s to <2 x i7>
@@ -99,6 +109,8 @@
   ret <2 x i7> %r
 }
 
+; negative test - the shift is too big for the narrow type
+
 define <2 x i7> @trunc_lshr_big_shift(<2 x i16> %x) {
 ; CHECK-LABEL: @trunc_lshr_big_shift(
 ; CHECK-NEXT:    [[S:%.*]] = lshr <2 x i16> [[X:%.*]], <i16 7, i16 7>
@@ -112,11 +124,13 @@
   ret <2 x i7> %r
 }
 
+; High bits could also be set rather than cleared.
+
 define i6 @or_trunc_lshr(i8 %x) {
 ; CHECK-LABEL: @or_trunc_lshr(
-; CHECK-NEXT:    [[S:%.*]] = lshr i8 [[X:%.*]], 1
-; CHECK-NEXT:    [[T:%.*]] = trunc i8 [[S]] to i6
-; CHECK-NEXT:    [[R:%.*]] = or i6 [[T]], -32
+; CHECK-NEXT:    [[TMP1:%.*]] = trunc i8 [[X:%.*]] to i6
+; CHECK-NEXT:    [[TMP2:%.*]] = lshr i6 [[TMP1]], 1
+; CHECK-NEXT:    [[R:%.*]] = or i6 [[TMP2]], -32
 ; CHECK-NEXT:    ret i6 [[R]]
 ;
   %s = lshr i8 %x, 1
@@ -127,9 +141,9 @@
 
 define i6 @or_trunc_lshr_more(i8 %x) {
 ; CHECK-LABEL: @or_trunc_lshr_more(
-; CHECK-NEXT:    [[S:%.*]] = lshr i8 [[X:%.*]], 4
-; CHECK-NEXT:    [[T:%.*]] = trunc i8 [[S]] to i6
-; CHECK-NEXT:    [[R:%.*]] = or i6 [[T]], -4
+; CHECK-NEXT:    [[TMP1:%.*]] = trunc i8 [[X:%.*]] to i6
+; CHECK-NEXT:    [[TMP2:%.*]] = lshr i6 [[TMP1]], 4
+; CHECK-NEXT:    [[R:%.*]] = or i6 [[TMP2]], -4
 ; CHECK-NEXT:    ret i6 [[R]]
 ;
   %s = lshr i8 %x, 4
@@ -138,6 +152,8 @@
   ret i6 %r
 }
 
+; negative test - need all high bits to be undemanded
+
 define i6 @or_trunc_lshr_small_mask(i8 %x) {
 ; CHECK-LABEL: @or_trunc_lshr_small_mask(
 ; CHECK-NEXT:    [[S:%.*]] = lshr i8 [[X:%.*]], 4