Cyclic Redundancy Codes (CRCs) provide a first line of defense against data corruption in many networks. Unfortunately, many commonly used CRC polynomials provide significantly less error detection capability than they might. An exhaustive exploration reveals that most previously published CRC polynomials are either inferior to alternatives or are only good choices for particular message lengths. Unfortunately these shortcomings and limitations often seem to be overlooked. This paper describes a polynomial selection process for embedded network applications and proposes a set of good general-purpose polynomials. A set of 35 new polynomials in addition to 13 previously published polynomials provides good performance for 3- to 16-bit CRCs for data word lengths up to 2048 bits.