This paper analyzes transmit antenna selection (TAS) under Rayleigh flat fading for BPSK/QPSK modulations in multiple-input multiple-output wiretap channels, also termed as multiple-input multiple-output multiple-eavesdropper (MIMOME) channels. In our protocol, a single antenna is selected to transmit the secret message and selection combing (SC) or maximal-ratio combing (MRC) is utilized at the legitimate receiver or the eavesdropper. Novel closed-form expressions for the ergodic secrecy rates are derived to approximate the exact values, which hold high precision and compact forms. Besides theoretical derivations, simulations are provided to demonstrate the feasibility and validity of the proposed formulas.