Wheel (at the moment). It appears to be a conversion (from the original tiller) and I plan on converting back to tiller.
I wonder about the cutter rig--- I have a bail on the mast in about the right location and a deck fitting aft of the bowsprit but no sign of running backstays so I'm not sure if mine was cutter rigged originally or not. I do know that my sail plan/rig dimensions do not match what is listed on the Soverel 33 site (the table for "other" Soverel designs)....
Even though our Soverel 30 was originally rigged as a cutter & we have all the standing rigging, some years ago, before we bought it, she started being used as just a sloop with a Hood roller furling unit, jibs, genoas. This works well for us, as it frees us the foredeck space to carry a dinghy. Interesting regarding the listed specifications, as our boat too does not match exactly the Soverel database which I want to correct. It shows that our boat would have been built later than 1974, though all the documentation we got with her indicates that she is a 1974 Soverel 30 Mk III. We do have a letter from Bill Soverel to the original owner confirming the hull number, so I should be able to clarify the discrepancies in the what years cutters/sloops, fixed/swing keels, & Bill/Mark Soverel designs were built.
I'm leaving this afternoon for a week cruise with two friends from San Carlos Mexico across the Sea of Cortez to Santa Rosalia and Conception Bay (Bahia de Concepcion)