diff --git a/xls/passes/arith_simplification_pass.cc b/xls/passes/arith_simplification_pass.cc
index 6d06e247db..f3532d51f0 100644
--- a/xls/passes/arith_simplification_pass.cc
+++ b/xls/passes/arith_simplification_pass.cc
@@ -1231,6 +1231,22 @@ absl::StatusOr<bool> MatchArithPatterns(int64_t opt_level, Node* n,
     return true;
   }
 
+  // Logical shift of a 1-bit value:
+  //   shll(y:bits[1], amt) == y & (amt == 0)
+  //   shrl(y:bits[1], amt) == y & (amt == 0)
+  //
+  // A 1-bit logical shift by a nonzero amount produces zero, and a shift by
+  // zero is a no-op.
+  if ((n->op() == Op::kShll || n->op() == Op::kShrl) &&
+      n->operand(0)->BitCountOrDie() == 1) {
+    VLOG(2) << "FOUND: logical shift of 1-bit value";
+    XLS_ASSIGN_OR_RETURN(Node * amt_is_zero,
+                         CompareLiteral(n->operand(1), 0, Op::kEq));
+    std::vector<Node*> args = {n->operand(0), amt_is_zero};
+    XLS_RETURN_IF_ERROR(n->ReplaceUsesWithNew<NaryOp>(args, Op::kAnd).status());
+    return true;
+  }
+
   // An arithmetic shift-right of a 1-bit value is a no-op.
   if (n->op() == Op::kShra && n->operand(0)->BitCountOrDie() == 1) {
     VLOG(2) << "FOUND: arithmetic shift-right of 1-bit value";
diff --git a/xls/passes/arith_simplification_pass_test.cc b/xls/passes/arith_simplification_pass_test.cc
index e0e6adddfc..6f38a57e1a 100644
--- a/xls/passes/arith_simplification_pass_test.cc
+++ b/xls/passes/arith_simplification_pass_test.cc
@@ -2170,6 +2170,32 @@ TEST_F(ArithSimplificationPassTest, GuardedShiftOperationLowLimit) {
   EXPECT_THAT(f->return_value(), m::Shll(m::Param("x"), m::Select()));
 }
 
+TEST_F(ArithSimplificationPassTest, LogicalShiftLeftOfOneBitUnknownAmount) {
+  auto p = CreatePackage();
+  FunctionBuilder fb(TestName(), p.get());
+  BValue amt = fb.Param("amt", p->GetBitsType(10));
+  BValue y = fb.Param("y", p->GetBitsType(1));
+  fb.Shll(y, amt);
+  XLS_ASSERT_OK_AND_ASSIGN(Function * f, fb.Build());
+  ScopedVerifyEquivalence sve(f, kProverTimeout);
+  ASSERT_THAT(Run(p.get()), IsOkAndHolds(true));
+  EXPECT_THAT(f->return_value(),
+              m::And(m::Param("y"), m::Eq(m::Param("amt"), m::Literal(0))));
+}
+
+TEST_F(ArithSimplificationPassTest, LogicalShiftRightOfOneBitUnknownAmount) {
+  auto p = CreatePackage();
+  FunctionBuilder fb(TestName(), p.get());
+  BValue amt = fb.Param("amt", p->GetBitsType(10));
+  BValue y = fb.Param("y", p->GetBitsType(1));
+  fb.Shrl(y, amt);
+  XLS_ASSERT_OK_AND_ASSIGN(Function * f, fb.Build());
+  ScopedVerifyEquivalence sve(f, kProverTimeout);
+  ASSERT_THAT(Run(p.get()), IsOkAndHolds(true));
+  EXPECT_THAT(f->return_value(),
+              m::And(m::Param("y"), m::Eq(m::Param("amt"), m::Literal(0))));
+}
+
 TEST_F(ArithSimplificationPassTest, UMulCompare) {
   auto p = CreatePackage();
   FunctionBuilder fb(TestName(), p.get());