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We study the birational geometry of $\bar{M}_{3,1}$ and $\bar{M}_{4,1}$. Inparticular, we pose a pointed analogue of the Slope Conjecture and prove it inthese low-genus cases. Using variation of GIT, we construct birationalcontractions of these spaces in which certain divisors of interest -- thepointed Brill-Noether divisors -- are contracted. As a consequence, we see thatthese pointed Brill-Noether divisors generate extremal rays of the effectivecones for these spaces.

Birational Contractions of $\bar{M}_{3,1}$ and $\bar{M}_{4,1}$