diff --git a/src/kani-compiler/src/codegen_cprover_gotoc/codegen/rvalue.rs b/src/kani-compiler/src/codegen_cprover_gotoc/codegen/rvalue.rs
index b90e661046c1..21dd75e7f0d2 100644
--- a/src/kani-compiler/src/codegen_cprover_gotoc/codegen/rvalue.rs
+++ b/src/kani-compiler/src/codegen_cprover_gotoc/codegen/rvalue.rs
@@ -447,6 +447,8 @@ impl<'tcx> GotocCtx<'tcx> {
                     e.member("case", &self.symbol_table).cast_to(self.codegen_ty(res_ty))
                 }
                 TagEncoding::Niche { dataful_variant, niche_variants, niche_start } => {
+                    // This code follows the logic in the cranelift codegen backend:
+                    // https://github.com/rust-lang/rust/blob/05d22212e89588e7c443cc6b9bc0e4e02fdfbc8d/compiler/rustc_codegen_cranelift/src/discriminant.rs#L116
                     let offset = match &layout.fields {
                         FieldsShape::Arbitrary { offsets, .. } => offsets[0].bytes_usize(),
                         _ => unreachable!("niche encoding must have arbitrary fields"),
@@ -457,8 +459,7 @@ impl<'tcx> GotocCtx<'tcx> {
                     let relative_discr = if *niche_start == 0 {
                         niche_val
                     } else {
-                        // This should be a wrapping sub.
-                        niche_val.sub(Expr::int_constant(*niche_start, discr_ty.clone()))
+                        wrapping_sub(&niche_val, *niche_start)
                     };
                     let relative_max =
                         niche_variants.end().as_u32() - niche_variants.start().as_u32();
@@ -467,8 +468,7 @@ impl<'tcx> GotocCtx<'tcx> {
                     } else {
                         relative_discr
                             .clone()
-                            .cast_to(Type::unsigned_int(64))
-                            .le(Expr::int_constant(relative_max, Type::unsigned_int(64)))
+                            .le(Expr::int_constant(relative_max, relative_discr.typ().clone()))
                     };
                     let niche_discr = {
                         let relative_discr = if relative_max == 0 {
@@ -1223,3 +1223,30 @@ impl<'tcx> GotocCtx<'tcx> {
         }
     }
 }
+
+/// Perform a wrapping subtraction of an Expr with a constant "expr - constant"
+/// where "-" is wrapping subtraction, i.e., the result should be interpreted as
+/// an unsigned value (2's complement).
+fn wrapping_sub(expr: &Expr, constant: u128) -> Expr {
+    // While the wrapping subtraction can be done through a regular subtraction
+    // and then casting the result to an unsigned, doing so may result in CBMC
+    // flagging the operation with a signed to unsigned overflow failure (see
+    // https://github.com/model-checking/kani/issues/356).
+    // To avoid those overflow failures, the wrapping subtraction operation is
+    // computed as:
+    //   if expr >= constant {
+    //       // result is positive, so overflow may not occur
+    //       expr - constant
+    //   } else {
+    //       // compute the 2's complement to avoid overflow
+    //       expr - constant + 2^32
+    //   }
+    let s64 = Type::signed_int(64);
+    let expr = expr.clone().cast_to(s64.clone());
+    let twos_complement: i64 = u32::MAX as i64 + 1 - i64::try_from(constant).unwrap();
+    let constant = Expr::int_constant(constant, s64.clone());
+    expr.clone().ge(constant.clone()).ternary(
+        expr.clone().sub(constant),
+        expr.plus(Expr::int_constant(twos_complement, s64.clone())),
+    )
+}
diff --git a/tests/kani/Enum/neg_discriminant.rs b/tests/kani/Enum/neg_discriminant.rs
new file mode 100644
index 000000000000..598445f78319
--- /dev/null
+++ b/tests/kani/Enum/neg_discriminant.rs
@@ -0,0 +1,29 @@
+// Copyright Amazon.com, Inc. or its affiliates. All Rights Reserved.
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+// This test checks that enums with negative discriminants are handled correctly
+
+enum Foo {
+    A = -500,
+    B = -200,
+    C = -100,
+    D = 0,
+    E = 1,
+    F = 256,
+}
+
+#[kani::proof]
+fn check_negative_discriminant() {
+    let a = Some(Foo::A);
+    let b = Some(Foo::B);
+    let c = Some(Foo::C);
+    let d = Some(Foo::D);
+    let e = Some(Foo::E);
+    let f = Some(Foo::F);
+    let _ = assert!(matches!(a, Some(Foo::A)));
+    let _ = assert!(matches!(b, Some(Foo::B)));
+    let _ = assert!(matches!(c, Some(Foo::C)));
+    let _ = assert!(matches!(d, Some(Foo::D)));
+    let _ = assert!(matches!(e, Some(Foo::E)));
+    let _ = assert!(matches!(f, Some(Foo::F)));
+}
diff --git a/tests/kani/LexicographicCmp/main.rs b/tests/kani/LexicographicCmp/main.rs
new file mode 100644
index 000000000000..1e82389ea2e1
--- /dev/null
+++ b/tests/kani/LexicographicCmp/main.rs
@@ -0,0 +1,10 @@
+// Copyright Amazon.com, Inc. or its affiliates. All Rights Reserved.
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+// This test checks that lexicographic comparison is handled correctly
+
+#[kani::proof]
+fn check_lexicographic_cmp() {
+    assert!([1, 2, 3] < [1, 3, 4]);
+    assert!("World" >= "Hello");
+}