My memory is only slightly different...and I could be wrong (I'm not currently in front of the game). 3rd through Early 7th all come up as three year deals. Some late 2nd might also be 3 year deals. Mid to late 7th are two year deals. The UDFAs are one-year deals. I'm not exactly sure where (or why) that cutoff is in the 7th round between 3 and 2 year deals, but I think it is around pick 200. I know I have had early 7th rounders sign to 3 year deals.
The problem with one and two year deals is that you don't get the benefit of that 4th year Restricted Free Agent. The RFA, for me, makes a 3 year deal as good as (perhaps better than) a 4-7 year deal. You either get 1) that person back another year at a pretty good price, 2) some draft picks, or 3) a longer-term contract a bit lower than you could have gotten on your own. I've noticed a level 4 tender on that 90+ potential will keep the competing offer that you have to match reasonably low (presumably because that team is also having to calculate the loss of a 1st and 3rd pick.)