The standard Gaussian approximation (SGA) for error analysis of direct-sequence code-division multiple-access (DS-CDMA) systems is very optimistic in many cases. Improved Gaussian approximation (IGA) is a technique that produces accurate error probabilities, but is still computationally intensive. Simplified IGA (SIGA) has complexity similar to that of SGA and, at the same time, provides sufficient accuracy. In this paper, we consider SIGA for DS-CDMA systems employing random sequences in a band-limited scenario. The validity of IGA for band-limited systems is established in a rigorous mathematical sense. Then a key parameter in SIGA is derived via a frequency-domain approach. Applications to a number of typical chip waveforms, including the popular sinc and raised-cosine pulses, are investigated. Performance comparison with IGA-based lower and upper bounds shows that SIGA yields very accurate probability of error.