Orthogonal frequency division multiplexing (OFDM) is highly sensitive to frequency offset since it induces inter-carrier interference (ICI). Fortunately, the pulse shaping filter method has proven its potential to reduce ICI without the cost of increasing the complexity of the OFDM modem. In order to improve the OFDM tolerance against the oscillator frequency detuning, we introduce the better than double jump 2 (BTDJ2) pulse. It is characterized by one additional design parameter apart from the roll-off factor. In addition, the improved filter is optimized following a representative system configuration. The BTDJ2 is compared with other novel pulses in terms of signal to noise ratio (SNR) and frequency offset requirements for a well known practical forward error correction (FEC) limit. Further, complexity evaluation of the BTDJ2 and other novel pulses is done in terms of the average elapsed convolution time. In general, the sub-optimum BTDJ2 outperforms other novel pulses in terms of the bit error rate (BER) and complexity.