Voice-crossing in First Species Counterpoint

Question

In two-part counterpoint, is it okay for the counterpoint and cantus firmus voices to cross?

Transferred from: Few Questions on Counterpoint in the Tradition of Johan Fux

Answer 1

Generally, contrary motion is favored over direct or similar motion. Contrary motion is typically more interesting, and in some cases facilitates easier voice leading. In such cases, it is acceptable for the voices to cross.

Transferred from: Few Questions on Counterpoint in the Tradition of Johan Fux

Answer 2

If you're going specifically from Fux's teaching he states that you should try not to have the voices cross unless both voices are heading towards each other and they absolutely have to cross to avoid breaking other rules like parallel perfect consonants and diminished 5ths.

I take this from The Study of Counterpoint, written by Fux himself