Alice can probably verify this, but I have always heard that a certain amount of vibrato is not only desirable, but necessary.

First, vibrato gives life to a voice. A voice without some vibrato sounds flat and dead—hence, some vibrato is indeed desirable. Second, I've heard some singers and one voice teacher say that vibrato is a sort of "feedback mechanism" that keeps the voice zeroed in on the desired pitches. Someplace in your medulla (or thereabouts) something says "Too high," and lowers the pitch, then says "Too low," and raises the pitch, etc., all happening unconsciously and very quickly. Hence, vibrato is never "intended," it just happens naturally. What lends a certain credence to this "feedback" idea is that I've noticed that people whose voices are devoid of vibrato tend to sing slightly off-pitch (either sharp or flat, but usually flat) most of the time.

Don't try for vibrato, just let it happen. It'll come. But if you don't want it—well, I don't know what you can do about that. But a wide, slow vibrato (wobble) isn't good. This seems to indicate that something isn't working right. Probably the first place to look would be breath support.

Don Firth