Can I tactfully change my mind after agreeing to do an independent study with a professor? I recently asked two professors by email if I could do an independent study with them. Both of them responded, saying that they can sponsor me for the study. As soon as I received the first professor's response, I replied, saying that I wanted to work with him and scheduling a face-to-face meeting.

Now that both professors have responded, though, I think I would enjoy working with the second professor more. Would it be appropriate for me to tell the first professor that I changed my mind, or would it be wrong to take back the commitment I already gave him? If it would be appropriate to change my mind, how can I handle the situation tactfully?

Although I would prefer to work with the second professor, I know that I would enjoy working with either of them, so I'll be fine if it's too late to change my mind.



Edit: Here is some more information about my specific situation.

I am planning on doing the same project with either professor. I am currently writing the music for a video game, and I would be working with the professors to produce the music and create a graded portfolio. I haven't worked out any specific details with either professor.

Both professors are music professors who have specific knowledge about music technology. The reason I would prefer working with the second professor is because I know he has expert knowledge of the software I'm using to produce the music. In addition, he is skilled with the genres of music I'm producing as well as writing film scores. I'm not sure how much the first professor knows about these specific topics.
Do you have a project already lined up ? it sounds like your meeting with the first professor would be to discuss topics for the study. In any case, if no financial agreement has been reached, I see no harm in talking with both professors and then making a decision based on what happens in those meetings. I disagree with @aeismail that you've given a formal commitment at this stage. 

You didn't say though why you'd prefer to work with the second professor prior to having a meeting ? is it the subject matter ? general rapport ?