Control for variable in within-subjects design


I'm currently analyzing some data that is intended to test cognitive styles and abilities as they pertain to performance on a test. What I want to do is control for spatial ability (covariate) when comparing spatial cognitive style (IV) with the test score (DV). All of these variables are within-subject variables--i.e., each Ss completed all three tasks.

My question is, can I use a simple linear regression model to do this, i.e., (score ~ spatial ability + spatial style)? Or do I need to use a mixed-model?

Thanks all!