If you're talking about opioids, which are well known for their constipating effects, all of them appear to cause about the same amount of constipation.

Perhaps the best thing is to do is to do what you can relieve it. You can do that by drinking alot of water, by going on walks, if you can do that, to get that area moving, by having fiber in your diet and by avoiding constipating foods and by occasionally taking stool softeners and laxatives. 

Find a list of constipating foods here and a list of foods that might be able to reduce constipation here. One webpage suggested the psyllium fiber may make things worse. 

You also might want to try an exercise that really works well for me. When you're sitting on the toilet put your hands on the outside of your knees and then press with your knees outwards against your hands. This can really help and it does it without you having to strain and possibly cause hemorrhoids. 

Good luck! 

Good luck!