diff --git a/xls/passes/BUILD b/xls/passes/BUILD
index 926968aa4f..e49ac35946 100644
--- a/xls/passes/BUILD
+++ b/xls/passes/BUILD
@@ -1107,6 +1107,7 @@ cc_library(
         "@com_google_absl//absl/log:check",
         "@com_google_absl//absl/status:statusor",
         "@com_google_absl//absl/strings:str_format",
+        "@com_google_absl//absl/types:span",
         "//xls/common:module_initializer",
         "//xls/common/status:status_macros",
         "//xls/ir",
@@ -2421,6 +2422,7 @@ cc_test(
         "//xls/ir:function_builder",
         "//xls/ir:ir_matcher",
         "//xls/ir:ir_test_base",
+        "//xls/solvers:z3_ir_equivalence_testutils",
         "@com_google_googletest//:gtest",
     ],
 )
diff --git a/xls/passes/bdd_simplification_pass.cc b/xls/passes/bdd_simplification_pass.cc
index c2e2fbbcdc..3be600b793 100644
--- a/xls/passes/bdd_simplification_pass.cc
+++ b/xls/passes/bdd_simplification_pass.cc
@@ -28,6 +28,7 @@
 #include "absl/log/log.h"
 #include "absl/status/statusor.h"
 #include "absl/strings/str_format.h"
+#include "absl/types/span.h"
 #include "xls/common/module_initializer.h"
 #include "xls/common/status/status_macros.h"
 #include "xls/ir/bits.h"
@@ -333,6 +334,35 @@ absl::StatusOr<bool> SimplifyNode(Node* node, const QueryEngine& query_engine,
     return true;
   }
 
+  // Simplify kPrioritySelect operations where the selector is known to have at
+  // least one set bit.
+  if (NarrowingEnabled(opt_level) && node->Is<PrioritySelect>() &&
+      query_engine.AtLeastOneBitTrue(node->As<PrioritySelect>()->selector())) {
+    PrioritySelect* sel = node->As<PrioritySelect>();
+
+    int64_t last_bit = 0;
+    std::vector<TreeBitLocation> trailing_bits;
+    for (; last_bit < sel->selector()->BitCountOrDie() - 1; ++last_bit) {
+      trailing_bits.push_back(TreeBitLocation(sel->selector(), last_bit));
+      if (query_engine.AtLeastOneTrue(trailing_bits)) {
+        break;
+      }
+    }
+    DCHECK(last_bit < sel->selector()->BitCountOrDie() - 1 ||
+           query_engine.AtLeastOneTrue(trailing_bits));
+
+    XLS_ASSIGN_OR_RETURN(Node * new_selector,
+                         node->function_base()->MakeNode<BitSlice>(
+                             node->loc(), sel->selector(),
+                             /*start=*/0, /*width=*/last_bit));
+    absl::Span<Node* const> new_cases = sel->cases().subspan(0, last_bit);
+    Node* new_default = sel->get_case(last_bit);
+    XLS_RETURN_IF_ERROR(node->ReplaceUsesWithNew<PrioritySelect>(
+                                new_selector, new_cases, new_default)
+                            .status());
+    return true;
+  }
+
   return false;
 }
 
diff --git a/xls/passes/bdd_simplification_pass_test.cc b/xls/passes/bdd_simplification_pass_test.cc
index 1f2cfb212c..6fdccff64d 100644
--- a/xls/passes/bdd_simplification_pass_test.cc
+++ b/xls/passes/bdd_simplification_pass_test.cc
@@ -31,6 +31,7 @@
 #include "xls/ir/package.h"
 #include "xls/passes/optimization_pass.h"
 #include "xls/passes/pass_base.h"
+#include "xls/solvers/z3_ir_equivalence_testutils.h"
 
 namespace m = ::xls::op_matchers;
 
@@ -122,6 +123,46 @@ TEST_F(BddSimplificationPassTest, RemoveRedundantOneHot) {
   EXPECT_THAT(f->return_value(), m::Concat(m::Eq(), m::Concat()));
 }
 
+TEST_F(BddSimplificationPassTest, RemoveRedundantPrioritySelectCases) {
+  auto p = CreatePackage();
+  FunctionBuilder fb(TestName(), p.get());
+  BValue x = fb.Param("x", p->GetBitsType(8));
+  BValue a = fb.Param("a", p->GetBitsType(24));
+  BValue b = fb.Param("b", p->GetBitsType(24));
+  BValue c = fb.Param("c", p->GetBitsType(24));
+  BValue d = fb.Param("d", p->GetBitsType(24));
+  BValue x_ge_5 = fb.UGe(x, fb.Literal(UBits(5, 8)));
+  BValue x_le_42 = fb.ULe(x, fb.Literal(UBits(42, 8)));
+  BValue x_eq_8 = fb.Eq(x, fb.Literal(UBits(8, 8)));
+  fb.PrioritySelect(fb.Concat({x_eq_8, x_ge_5, x_le_42}), /*cases=*/{a, b, c},
+                    /*default_value=*/d);
+  XLS_ASSERT_OK_AND_ASSIGN(Function * f, fb.Build());
+
+  solvers::z3::ScopedVerifyEquivalence sve{f};
+  EXPECT_THAT(Run(f), IsOkAndHolds(true));
+  EXPECT_THAT(f->return_value(),
+              m::PrioritySelect(m::BitSlice(m::Concat()), {m::Param("a")},
+                                m::Param("b")));
+}
+
+TEST_F(BddSimplificationPassTest, PreserveNonRedundantPrioritySelectCases) {
+  auto p = CreatePackage();
+  FunctionBuilder fb(TestName(), p.get());
+  BValue x = fb.Param("x", p->GetBitsType(8));
+  BValue a = fb.Param("a", p->GetBitsType(24));
+  BValue b = fb.Param("b", p->GetBitsType(24));
+  BValue c = fb.Param("c", p->GetBitsType(24));
+  BValue d = fb.Param("d", p->GetBitsType(24));
+  BValue x_ge_5 = fb.UGe(x, fb.Literal(UBits(5, 8)));
+  BValue x_lt_3 = fb.ULt(x, fb.Literal(UBits(3, 8)));
+  BValue x_eq_3 = fb.Eq(x, fb.Literal(UBits(3, 8)));
+  fb.PrioritySelect(fb.Concat({x_eq_3, x_ge_5, x_lt_3}), /*cases=*/{a, b, c},
+                    /*default_value=*/d);
+  XLS_ASSERT_OK_AND_ASSIGN(Function * f, fb.Build());
+
+  EXPECT_THAT(Run(f), IsOkAndHolds(false));
+}
+
 TEST_F(BddSimplificationPassTest, ConvertTwoWayOneHotSelect) {
   auto p = CreatePackage();
   XLS_ASSERT_OK_AND_ASSIGN(Function * f, ParseFunction(R"(