Quite often in my own songs I'll intentionally avoid a perfect rhyme and use a part rhyme instead - because it says what I want said better, but also because I prefer the slight discordance involved.

For example in one song I've a line (about some former resistance fighters becoming politicians who do well out of the new regime)where the perfect rhyme would have been :

"For some it ended in a life so splendid"

But instead I chose to have it as

"For some it ended in a life resplendent"

which I think sounds better, as well as maybe giving more of a picture.

Again, quoting myself, one of the cheekiest rhymes I've used is at the end of the second and fourth lines of this verse. I think it just about works, by which I mean it doesn't sound as though I've has to wrench what I'm saying around in order to get it:

There are hard days and good days.
And days to remember, winter, summer, spring and fall;
And the best days are hard days, as often times as not
And the day we are born, that's the hardest day of all.