diff --git a/llvm/lib/Analysis/ValueTracking.cpp b/llvm/lib/Analysis/ValueTracking.cpp
--- a/llvm/lib/Analysis/ValueTracking.cpp
+++ b/llvm/lib/Analysis/ValueTracking.cpp
@@ -3321,10 +3321,18 @@
       return Tmp;
     }
 
-    case Instruction::Trunc:
-      // FIXME: it's tricky to do anything useful for this, but it is an
-      // important case for targets like X86.
+    case Instruction::Trunc: {
+      // If the input contained enough sign bits that some remain after the
+      // truncation, then we can make use of that. Otherwise we don't know
+      // anything.
+      Tmp = ComputeNumSignBits(U->getOperand(0), Depth + 1, Q);
+      unsigned OperandTyBits = Q.DL.getTypeSizeInBits(U->getOperand(0)->getType());
+      if (Tmp > (OperandTyBits - TyBits)) {
+        return Tmp - (OperandTyBits - TyBits);
+      }
+
       break;
+    }
 
     case Instruction::ExtractElement:
       // Look through extract element. At the moment we keep this simple and
diff --git a/llvm/test/Transforms/InstCombine/high-bit-signmask-with-trunc.ll b/llvm/test/Transforms/InstCombine/high-bit-signmask-with-trunc.ll
--- a/llvm/test/Transforms/InstCombine/high-bit-signmask-with-trunc.ll
+++ b/llvm/test/Transforms/InstCombine/high-bit-signmask-with-trunc.ll
@@ -138,7 +138,7 @@
 ; CHECK-LABEL: @n10(
 ; CHECK-NEXT:    [[T0_NEG:%.*]] = ashr i64 [[X:%.*]], 63
 ; CHECK-NEXT:    [[T1_NEG:%.*]] = trunc i64 [[T0_NEG]] to i32
-; CHECK-NEXT:    [[R:%.*]] = add i32 [[T1_NEG]], 1
+; CHECK-NEXT:    [[R:%.*]] = add nsw i32 [[T1_NEG]], 1
 ; CHECK-NEXT:    ret i32 [[R]]
 ;
   %t0 = lshr i64 %x, 63
diff --git a/llvm/test/Transforms/InstCombine/negated-bitmask.ll b/llvm/test/Transforms/InstCombine/negated-bitmask.ll
--- a/llvm/test/Transforms/InstCombine/negated-bitmask.ll
+++ b/llvm/test/Transforms/InstCombine/negated-bitmask.ll
@@ -71,7 +71,7 @@
 ; CHECK-NEXT:    [[TMP1:%.*]] = shl i64 [[A0:%.*]], 48
 ; CHECK-NEXT:    [[TMP2:%.*]] = ashr i64 [[TMP1]], 63
 ; CHECK-NEXT:    [[TMP3:%.*]] = trunc i64 [[TMP2]] to i8
-; CHECK-NEXT:    [[NEG:%.*]] = add i8 [[TMP3]], 10
+; CHECK-NEXT:    [[NEG:%.*]] = add nsw i8 [[TMP3]], 10
 ; CHECK-NEXT:    ret i8 [[NEG]]
 ;
   %shift = lshr i64 %a0, 15
@@ -86,7 +86,7 @@
 ; CHECK-NEXT:    [[TMP1:%.*]] = shl i64 [[A0:%.*]], 48
 ; CHECK-NEXT:    [[TMP2:%.*]] = ashr i64 [[TMP1]], 63
 ; CHECK-NEXT:    [[TMP3:%.*]] = trunc i64 [[TMP2]] to i8
-; CHECK-NEXT:    [[NARROW:%.*]] = add i8 [[TMP3]], 10
+; CHECK-NEXT:    [[NARROW:%.*]] = add nsw i8 [[TMP3]], 10
 ; CHECK-NEXT:    [[NEG:%.*]] = zext i8 [[NARROW]] to i32
 ; CHECK-NEXT:    ret i32 [[NEG]]
 ;