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
@@ -994,30 +994,26 @@
   bool ShiftAmtIsConstant = Known.isConstant();
   bool MaxShiftAmtIsOutOfRange = Known.getMaxValue().uge(BitWidth);
 
-  if (ShiftAmtIsConstant) {
-    Known = KF(Known2, Known);
-
-    // If the known bits conflict, this must be an overflowing left shift, so
-    // the shift result is poison. We can return anything we want. Choose 0 for
-    // the best folding opportunity.
-    if (Known.hasConflict())
-      Known.setAllZero();
+  // Use the KF callback to get an initial knownbits approximation.
+  Known = KF(Known2, Known);
 
+  // If the known bits conflict, this must be an overflowing left shift, so
+  // the shift result is poison.
+  if (Known.hasConflict()) {
+    Known.resetAll();
     return;
   }
 
+  // Constant shift amount - we're not going to improve on this.
+  if (ShiftAmtIsConstant)
+    return;
+
   // If the shift amount could be greater than or equal to the bit-width of the
   // LHS, the value could be poison, but bail out because the check below is
   // expensive.
   // TODO: Should we just carry on?
-  if (MaxShiftAmtIsOutOfRange) {
-    Known.resetAll();
+  if (MaxShiftAmtIsOutOfRange)
     return;
-  }
-
-  // It would be more-clearly correct to use the two temporaries for this
-  // calculation. Reusing the APInts here to prevent unnecessary allocations.
-  Known.resetAll();
 
   // If we know the shifter operand is nonzero, we can sometimes infer more
   // known bits. However this is expensive to compute, so be lazy about it and
@@ -1057,10 +1053,9 @@
         Known, KF(Known2, KnownBits::makeConstant(APInt(32, ShiftAmt))));
   }
 
-  // If the known bits conflict, the result is poison. Return a 0 and hope the
-  // caller can further optimize that.
+  // If the known bits conflict, the result is poison.
   if (Known.hasConflict())
-    Known.setAllZero();
+    Known.resetAll();
 }
 
 static void computeKnownBitsFromOperator(const Operator *I,
@@ -1232,10 +1227,6 @@
     };
     computeKnownBitsFromShiftOperator(I, DemandedElts, Known, Known2, Depth, Q,
                                       KF);
-    // Trailing zeros of a right-shifted constant never decrease.
-    const APInt *C;
-    if (match(I->getOperand(0), m_APInt(C)))
-      Known.Zero.setLowBits(C->countTrailingZeros());
     break;
   }
   case Instruction::LShr: {
@@ -1244,10 +1235,6 @@
     };
     computeKnownBitsFromShiftOperator(I, DemandedElts, Known, Known2, Depth, Q,
                                       KF);
-    // Leading zeros of a left-shifted constant never decrease.
-    const APInt *C;
-    if (match(I->getOperand(0), m_APInt(C)))
-      Known.Zero.setHighBits(C->countLeadingZeros());
     break;
   }
   case Instruction::AShr: {
diff --git a/llvm/lib/Support/KnownBits.cpp b/llvm/lib/Support/KnownBits.cpp
--- a/llvm/lib/Support/KnownBits.cpp
+++ b/llvm/lib/Support/KnownBits.cpp
@@ -187,6 +187,25 @@
     MinTrailingZeros = std::min(MinTrailingZeros, BitWidth);
   }
 
+  // If the maximum shift is in range, then find the common bits from all
+  // possible shifts.
+  APInt MaxShiftAmount = RHS.getMaxValue();
+  if (MaxShiftAmount.ult(BitWidth)) {
+    assert(MinShiftAmount.ult(MaxShiftAmount) && "Illegal shift range");
+    Known.Zero.setAllBits();
+    Known.One.setAllBits();
+    for (uint64_t ShiftAmt = MinShiftAmount.getZExtValue(),
+                  MaxShiftAmt = MaxShiftAmount.getZExtValue();
+         ShiftAmt <= MaxShiftAmt; ++ShiftAmt) {
+      KnownBits SpecificShift;
+      SpecificShift.Zero = LHS.Zero << ShiftAmt;
+      SpecificShift.One = LHS.One << ShiftAmt;
+      Known = KnownBits::commonBits(Known, SpecificShift);
+      if (Known.isUnknown())
+        break;
+    }
+  }
+
   Known.Zero.setLowBits(MinTrailingZeros);
   return Known;
 }
diff --git a/llvm/test/Transforms/InstSimplify/icmp-constant.ll b/llvm/test/Transforms/InstSimplify/icmp-constant.ll
--- a/llvm/test/Transforms/InstSimplify/icmp-constant.ll
+++ b/llvm/test/Transforms/InstSimplify/icmp-constant.ll
@@ -799,7 +799,7 @@
 
 define i1 @eq_shl_by_variable_produces_poison(i8 %x) {
 ; CHECK-LABEL: @eq_shl_by_variable_produces_poison(
-; CHECK-NEXT:    ret i1 false
+; CHECK-NEXT:    ret i1 poison
 ;
   %clear_high_bit = and i8 %x, 127                 ; 0x7f
   %set_next_high_bits = or i8 %clear_high_bit, 112 ; 0x70