I'm actually wearing a pair of jeans right now that used to be my husband's...he outgrew them, but the waist fit me, and since that's the only hard part to change I took a stab at it. They were Gap "loose fit", which I would assume is just about like the relaxed fit you're talking about. First, I took them in at the inseam, all the way up and over the crotch and down the other side. I sorta based it off another pair of jeans. That took out some of the unneeded space that guys need there, but girls don't.
Then, I put the jeans on inside out and pinned the outer seam until it was the fit that I like. When I cut off the extra fabric, I just zigzagged to keep it from fraying because I don't have a serger, and that's been working just fine. I wore them that way for a while, but the front part of the top of the jeans would always bunch up funny. So, just this morning actually, I made the final alterations that made them fit perfectly. I unpicked the waistband from the center out to the inner edge of the pockets. Then, I made a diagonal cut through the zipper to meet up with the old edge by the pocket corner. Then, I resewed the waistband as it had been before. I had to alter the zipper flaps a little to make up for the extra distance (there's extra distance because it's cut on a diagonal compared to how it was before...) that wouldn't fit into the old waistband, but it's hardly noticeable to do so. That took care of the extra bulging, and I'm quite happy with how they fit now.
It kinda sounds a little confusing, but I didn't find it to be too hard. Just kinda took each fit issue as it came, and we didn't have to throw out a $50 pair of jeans my husband only wore twice.
You may have to look out for things like topstitching on the seams, but I took these in so much that all the old seams went out the window anyway, other than right on the side of my hips. I'm sure it would also look nice to go back and topstitch the seams, but I haven't done so yet and they look fine! One thing to consider though is that men's jeans don't stretch like women's do, so you may not be able to make them quite as tight as they might normally be, but mine are fitted pretty well and they are still pretty easy to move around in.
Hope that helps some, if you haven't already found something to do with the jeans in question!