In recent research on collusion-secure fingerprint codes, some relaxation of the conventional security assumption (Marking Assumption) have been introduced from a viewpoint of reality in practical situations, and several fingerprint codes have been proposed under those assumptions. In this article, we consider such a relaxed assumption and give an extension of short 2-secure codes (under Marking Assumption) recently proposed by Nuida et al. (IEICE Trans. A, 2009) to our assumption. We perform theoretical and numerical evaluation of security and required code lengths. For example, to bound the error probability by 0.01% for 10,000 users, 162-bit, 220-bit and 329-bit lengths are sufficient even if each bit of the fingerprint codeword is either flipped (in addition to other collusion attacks) with probabilities 1%, 2.5% and 5%, respectively, or erased with probabilities 2%, 5% and 10%, respectively.