I don't know if you sing with accompaniment, but I've sometimes noticed singers almost being forced into awkward phrasing because of a rhythmic and demanding backing (even when they're playing the instrument themselves, sometimes).
I suspect it should be easier for an unaccompanied singer, but you have to be able to hear what you're doing when practising. My starting point is to make myself thoroughly comfortable with a basic version of the tune - no words, at this point. I then begin to work up the lyrics, a verse at a time, and if they sound "clunky" I abandon the tune and read them aloud till they settle into the rhythm of speech. And with that pattern in my mind, I go back to my basic tune and juggle it about until I'm happy with the result.
And if you do sing with instrument(s), perhaps think about freeing up the accompaniment so that the song dictates what happens, rather than the singer being dragged along in the wake of the musician(s).
Hope this might be of some help.