Compressing DICOM overlay data

How can I compress DICOM overlay data (6000:3000) image?

I am saving DICOM images as J2K, however the overlay image data remains uncompressed.

I have tried compressing the overlay data explicitly using RLE:

private RasterImage compressOverlay(RasterImage image)
{
var cmd = new ConvertSignedToUnsignedCommand(ConvertSignedToUnsignedCommandType.ShiftNegativeToZero);
if (image.OverlayCount > 0)
{
for (var overlayIndex = 0; overlayIndex < image.OverlayCount; overlayIndex++)
{
var overlayImage = image.GetOverlayImage(overlayIndex, RasterGetSetOverlayImageMode.Copy);
cmd.Run(overlayImage);
overlayImage.ChangeCompression(RasterCompression.Rle);
image.SetOverlayImage(overlayIndex, overlayImage, RasterGetSetOverlayImageMode.Copy);
}
}
return image;
}

However, upon saving the above image into DICOM dataset, the OverlayData element becomes uncompressed.

How can I persist the compressed overlay image to DICOM dataset? Better yet, is there any way to convert overlay images to J2K/JPG format? Section 8 (https://www.dabsoft.ch/dicom/5/8/) seems to indicate overlay data can be compressed.

brass9,
According to the DICOM Standard, overlay data is just uncompressed 1-bit image. It can't be compressed.