We present theoretical results pertaining to the ability of ℓ_p minimization to recover sparse and compressible signals from incomplete and noisy measurements. In particular, we extend the results of Candès, Romberg and Tao to the p < 1 case. Our results indicate that depending on the restricted isometry constants and the noise level, ℓ_p minimization with certain values of p < 1 provides better theoretical guarantees in terms of stability and robustness than ℓ₁ minimization does. This is especially true when the restricted isometry constants are relatively large.