diff --git a/include/Dialect/Polynomial/IR/BUILD b/include/Dialect/Polynomial/IR/BUILD
index d7acbe6b67..3d43d74d65 100644
--- a/include/Dialect/Polynomial/IR/BUILD
+++ b/include/Dialect/Polynomial/IR/BUILD
@@ -64,11 +64,17 @@ gentbl_cc_library(
     name = "attributes_inc_gen",
     tbl_outs = [
         (
-            ["-gen-attrdef-decls"],
+            [
+                "-gen-attrdef-decls",
+                "-attrdefs-dialect=polynomial",
+            ],
             "PolynomialAttributes.h.inc",
         ),
         (
-            ["-gen-attrdef-defs"],
+            [
+                "-gen-attrdef-defs",
+                "-attrdefs-dialect=polynomial",
+            ],
             "PolynomialAttributes.cpp.inc",
         ),
         (
diff --git a/include/Dialect/Polynomial/IR/PolynomialAttributes.td b/include/Dialect/Polynomial/IR/PolynomialAttributes.td
index 06a7f45e43..22b26356bd 100644
--- a/include/Dialect/Polynomial/IR/PolynomialAttributes.td
+++ b/include/Dialect/Polynomial/IR/PolynomialAttributes.td
@@ -3,8 +3,9 @@
 
 include "include/Dialect/Polynomial/IR/PolynomialDialect.td"
 
-include "mlir/IR/DialectBase.td"
 include "mlir/IR/AttrTypeBase.td"
+include "mlir/IR/BuiltinAttributes.td"
+include "mlir/IR/DialectBase.td"
 
 class Polynomial_Attr<string name, string attrMnemonic, list<Trait> traits = []>
     : AttrDef<Polynomial_Dialect, name, traits> {
@@ -46,26 +47,29 @@ def Ring_Attr : Polynomial_Attr<"Ring", "ring"> {
       #ring = #polynomial.ring<cmod=1234, ideal=#polynomial.polynomial<x**1024 + 1>>
   }];
 
-  // The extra cwidth parameter is required because, when the MLIR framework's
-  // StorageUniquer is determining whether to build a new instance of this
-  // attribute or reuse an existing one, it does an == comparison on the
-  // parameters, and comparing two APInts with different underlying bit widths
-  // leads to an assertion failure. By adding the container bit width as a
-  // parameter, that bit width is compared first and the rest of the check is
-  // skipped if the bit widths disagree. The custom builder and custom
-  // parser/printer ensures that cwidth is automatically inferred from cmod, and
-  // not printed or parsed, so that the cwidth parameter need not be known to the
-  // user.
-  let parameters = (ins "int64_t": $cwidth, "APInt": $cmod, "Polynomial":$ideal);
+  let parameters = (ins "IntegerAttr": $cmod, "Polynomial":$ideal);
 
   let builders = [
-    AttrBuilderWithInferredContext<(ins "APInt": $cmod, "Polynomial":$ideal), [{
-      return $_get(ideal.getContext(), cmod.getBitWidth(), cmod, ideal);
+    AttrBuilderWithInferredContext<
+        (ins "IntegerType":$type, "const APInt &": $cmod, "Polynomial":$ideal), [{
+      return $_get(
+        type.getContext(),
+        IntegerAttr::get(type, cmod.zextOrTrunc(type.getWidth())),
+        ideal
+      );
+    }]>,
+    AttrBuilderWithInferredContext<
+        (ins "const APInt &": $cmod, "Polynomial":$ideal), [{
+      return $_get(
+        ideal.getContext(),
+        IntegerAttr::get(IntegerType::get(ideal.getContext(), cmod.getBitWidth()), cmod),
+        ideal
+      );
     }]>
   ];
   let extraClassDeclaration = [{
     Polynomial ideal() const { return getIdeal(); }
-    APInt coefficientModulus() const { return getCmod(); }
+    APInt coefficientModulus() const { return getCmod().getValue(); }
   }];
 
   let skipDefaultBuilders = 1;
diff --git a/lib/Conversion/PolynomialToStandard/PolynomialToStandard.cpp b/lib/Conversion/PolynomialToStandard/PolynomialToStandard.cpp
index cf85cc0d53..49b22a4aaa 100644
--- a/lib/Conversion/PolynomialToStandard/PolynomialToStandard.cpp
+++ b/lib/Conversion/PolynomialToStandard/PolynomialToStandard.cpp
@@ -621,7 +621,8 @@ func::FuncOp PolynomialToStandard::buildPolynomialModFunc(FunctionType funcType,
   // division. The lowering must fail:
   auto divisor = ring.getIdeal();
   auto leadingCoef = divisor.getTerms().back().coefficient;
-  auto leadingCoefInverse = leadingCoef.multiplicativeInverse(ring.getCmod());
+  auto leadingCoefInverse =
+      leadingCoef.multiplicativeInverse(ring.coefficientModulus());
   // APInt signals no inverse by returning zero.
   if (leadingCoefInverse.isZero()) {
     signalPassFailure();
@@ -686,8 +687,8 @@ func::FuncOp PolynomialToStandard::buildPolynomialModFunc(FunctionType funcType,
   auto toTensorOp = builder.create<ToTensorOp>(inputType, whileOp.getResult(0));
   auto remainderModArg = builder.create<arith::ConstantOp>(
       inputType, DenseElementsAttr::get(
-                     inputType, APInt(inputType.getElementTypeBitWidth(),
-                                      ring.getCmod().getSExtValue())));
+                     inputType, ring.coefficientModulus().sextOrTrunc(
+                                    inputType.getElementTypeBitWidth())));
   auto remainderCoeffsRemOp = builder.create<arith::RemSIOp>(
       toTensorOp.getResult(), remainderModArg.getResult());
 
diff --git a/lib/Dialect/PolyExt/IR/PolyExtDialect.cpp b/lib/Dialect/PolyExt/IR/PolyExtDialect.cpp
index 9a072bb8cb..71b7d7aed2 100644
--- a/lib/Dialect/PolyExt/IR/PolyExtDialect.cpp
+++ b/lib/Dialect/PolyExt/IR/PolyExtDialect.cpp
@@ -33,13 +33,21 @@ polynomial::PolynomialType getPolynomialType(Type t) {
 LogicalResult CModSwitchOp::verify() {
   auto xRing = getPolynomialType(getX().getType()).getRing();
   auto outRing = getPolynomialType(getOutput().getType()).getRing();
-  auto outRingCmod = outRing.getCmod();
+  auto outRingCmod = outRing.getCmod().getValue();
+  auto xRingCmod = xRing.getCmod().getValue();
 
   if (xRing.getIdeal() != outRing.getIdeal()) {
     return emitOpError("input and output rings ideals must be the same");
   }
 
-  if (xRing.getCmod().ule(outRingCmod)) {
+  if (xRingCmod.getBitWidth() != outRingCmod.getBitWidth()) {
+    return emitOpError(
+        "input ring cmod and output ring cmod's have different bit widths; "
+        "consider annotating the types with `: i64` or similar, or using "
+        "the relevant builder on Ring_Attr");
+  }
+
+  if (xRingCmod.ule(outRingCmod)) {
     return emitOpError("input ring cmod must be larger than output ring cmod");
   }