diff --git a/mlir/lib/Dialect/SparseTensor/Transforms/SparseTensorConversion.cpp b/mlir/lib/Dialect/SparseTensor/Transforms/SparseTensorConversion.cpp
--- a/mlir/lib/Dialect/SparseTensor/Transforms/SparseTensorConversion.cpp
+++ b/mlir/lib/Dialect/SparseTensor/Transforms/SparseTensorConversion.cpp
@@ -582,8 +582,18 @@
       SmallVector<Value, 8> params;
       sizesFromPtr(rewriter, sizes, op, encSrc, srcType.cast<ShapedType>(),
                    src);
-      newParams(rewriter, params, op, encDst, kToCOO, sizes, src);
+      // Set up encoding with right mix of src and dst so that the two
+      // method calls can share most parameters, while still providing
+      // the correct sparsity information to either of them.
+      auto enc = SparseTensorEncodingAttr::get(
+          op->getContext(), encDst.getDimLevelType(), encDst.getDimOrdering(),
+          encSrc.getPointerBitWidth(), encSrc.getIndexBitWidth());
+      newParams(rewriter, params, op, enc, kToCOO, sizes, src);
       Value coo = genNewCall(rewriter, op, params);
+      params[3] = constantI32(
+          rewriter, loc, getOverheadTypeEncoding(encDst.getPointerBitWidth()));
+      params[4] = constantI32(
+          rewriter, loc, getOverheadTypeEncoding(encDst.getIndexBitWidth()));
       params[6] = constantI32(rewriter, loc, kFromCOO);
       params[7] = coo;
       rewriter.replaceOp(op, genNewCall(rewriter, op, params));
diff --git a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_convert.mlir b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_conversion_dyn.mlir
rename from mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_convert.mlir
rename to mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_conversion_dyn.mlir
diff --git a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_convert.mlir b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_conversion_ptr.mlir
rename from mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_convert.mlir
rename to mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_conversion_ptr.mlir
--- a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_convert.mlir
+++ b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_conversion_ptr.mlir
@@ -12,18 +12,22 @@
 // RUN: FileCheck %s
 
 #DCSR  = #sparse_tensor.encoding<{
-  dimLevelType = [ "compressed", "compressed" ]
+  dimLevelType = [ "compressed", "compressed" ],
+  pointerBitWidth = 8,
+  indexBitWidth = 8
 }>
 
 #DCSC  = #sparse_tensor.encoding<{
   dimLevelType = [ "compressed", "compressed" ],
-  dimOrdering = affine_map<(i,j) -> (j,i)>
+  dimOrdering = affine_map<(i,j) -> (j,i)>,
+  pointerBitWidth = 64,
+  indexBitWidth = 64
 }>
 
 //
 // Integration test that tests conversions between sparse tensors,
-// where the dynamic sizes of the shape of the enveloping tensor
-// may change (the actual underlying sizes obviously never change).
+// where the pointer and index sizes in the overhead storage change
+// in addition to layout.
 //
 module {
 
@@ -45,46 +49,36 @@
         [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0 ]> : tensor<32x64xf64>
     %t2 = tensor.cast %t1 : tensor<32x64xf64> to tensor<?x?xf64>
 
-    // Four dense to sparse conversions.
-    %1 = sparse_tensor.convert %t1 : tensor<32x64xf64> to tensor<?x?xf64, #DCSR>
-    %2 = sparse_tensor.convert %t1 : tensor<32x64xf64> to tensor<?x?xf64, #DCSC>
-    %3 = sparse_tensor.convert %t2 : tensor<?x?xf64> to tensor<?x?xf64, #DCSR>
-    %4 = sparse_tensor.convert %t2 : tensor<?x?xf64> to tensor<?x?xf64, #DCSC>
+    // Dense to sparse.
+    %1 = sparse_tensor.convert %t1 : tensor<32x64xf64> to tensor<32x64xf64, #DCSR>
+    %2 = sparse_tensor.convert %t1 : tensor<32x64xf64> to tensor<32x64xf64, #DCSC>
 
-    // Two cross conversions.
-    %5 = sparse_tensor.convert %3 : tensor<?x?xf64, #DCSR> to tensor<?x?xf64, #DCSC>
-    %6 = sparse_tensor.convert %4 : tensor<?x?xf64, #DCSC> to tensor<?x?xf64, #DCSR>
+    // Sparse to sparse.
+    %3 = sparse_tensor.convert %1 : tensor<32x64xf64, #DCSR> to tensor<32x64xf64, #DCSC>
+    %4 = sparse_tensor.convert %2 : tensor<32x64xf64, #DCSC> to tensor<32x64xf64, #DCSR>
 
     //
     // All proper row-/column-wise?
     //
     // CHECK: ( 1, 2, 3, 4, 5, 6, 7, -1 )
     // CHECK: ( 1, 4, 6, 2, 5, 3, 7, -1 )
-    // CHECK: ( 1, 2, 3, 4, 5, 6, 7, -1 )
-    // CHECK: ( 1, 4, 6, 2, 5, 3, 7, -1 )
     // CHECK: ( 1, 4, 6, 2, 5, 3, 7, -1 )
     // CHECK: ( 1, 2, 3, 4, 5, 6, 7, -1 )
     //
-    %m1 = sparse_tensor.values %1 : tensor<?x?xf64, #DCSR> to memref<?xf64>
-    %m2 = sparse_tensor.values %2 : tensor<?x?xf64, #DCSC> to memref<?xf64>
-    %m3 = sparse_tensor.values %3 : tensor<?x?xf64, #DCSR> to memref<?xf64>
-    %m4 = sparse_tensor.values %4 : tensor<?x?xf64, #DCSC> to memref<?xf64>
-    %m5 = sparse_tensor.values %5 : tensor<?x?xf64, #DCSC> to memref<?xf64>
-    %m6 = sparse_tensor.values %6 : tensor<?x?xf64, #DCSR> to memref<?xf64>
+    %m1 = sparse_tensor.values %1 : tensor<32x64xf64, #DCSR> to memref<?xf64>
+    %m2 = sparse_tensor.values %2 : tensor<32x64xf64, #DCSC> to memref<?xf64>
+    %m3 = sparse_tensor.values %3 : tensor<32x64xf64, #DCSC> to memref<?xf64>
+    %m4 = sparse_tensor.values %4 : tensor<32x64xf64, #DCSR> to memref<?xf64>
     call @dump(%m1) : (memref<?xf64>) -> ()
     call @dump(%m2) : (memref<?xf64>) -> ()
     call @dump(%m3) : (memref<?xf64>) -> ()
     call @dump(%m4) : (memref<?xf64>) -> ()
-    call @dump(%m5) : (memref<?xf64>) -> ()
-    call @dump(%m6) : (memref<?xf64>) -> ()
 
     // Release the resources.
-    sparse_tensor.release %1 : tensor<?x?xf64, #DCSR>
-    sparse_tensor.release %2 : tensor<?x?xf64, #DCSC>
-    sparse_tensor.release %3 : tensor<?x?xf64, #DCSR>
-    sparse_tensor.release %4 : tensor<?x?xf64, #DCSC>
-    sparse_tensor.release %5 : tensor<?x?xf64, #DCSC>
-    sparse_tensor.release %6 : tensor<?x?xf64, #DCSR>
+    sparse_tensor.release %1 : tensor<32x64xf64, #DCSR>
+    sparse_tensor.release %2 : tensor<32x64xf64, #DCSC>
+    sparse_tensor.release %3 : tensor<32x64xf64, #DCSC>
+    sparse_tensor.release %4 : tensor<32x64xf64, #DCSR>
 
     return
   }