Will lowering the dose of methadone help alleviate constipation?

I am on methadone and have severe constipation. The clinic nurse said I would have to significantly reduce the dose (70 - 80% over time) to get relief. I understand that it is long acting and builds up in your system but is that accurate? There would be no relief after going down 15-20 mg? Thanks!

: http://alcoholdrugstreatment.info/will-lowering-the-dose-of-methadone-help-alleviate-constipation-2