These rules governing the melodic flow of each counterpoint are common to every species. I'll add to the list, or clarify the wording, as I come to understand them better.
1. Forbidden skips: augmented fourth, major sixth (up or down), minor sixth (down only), seventh, any interval greater than an octave.
2. "Exposed" tritones are forbidden. That is, no run of notes in a single direction should be an augmented 4th from end to end.
[NOTE: Since all of these exercises are written in their natural modes, the special notes to watch out for are F and B-- an augmented fourth when taken together. There can be no jumps between F and B, and no runs that begin on one can end on the other. Beware of F and B!]
3. Leaps of an ascending minor sixth or octave, or a descending octave must be "recovered." That is, such a large skip must be followed immediately by a step back into the range covered by the leap. (Fux often "recovers" using a skip of a third back into the big leap.)
4. Do not repeat notes. (Though Fux makes many exceptions in Species One, repeated notes are rare in the other species.)
5. Avoid multiple skips in the same direction. (This is a guideline-- Fux contradicts this advice all the time. See, e.g., page 46, in the 2nd species phrygian example, he skips 4th, 5th, and 4th in the same direction: c-f-c'-f'.)