A time limit is also deterministic in some sense. Level settings used to be mainly time based, because computers at lower settings were no serious competition to decent players, but you don't necessarily want to wait for 30 seconds each move, so there were more casual and more serious levels.

Limiting the search depth is much more deterministic. At lower levels, it has hilarious results, and is pretty good at emulating beginning players (who know the rules, but have a limited skill of calculating moves ahead).

One problem with fixed search depth is that I think most good engines prefer to use dynamic search depth (where they sense that some positions need to be searched a bit deeper to reach a quiescent point), so they will be handicapped with a fix depth.