In this paper, a new method for power-efficient intersymbol interference-free transmission over the bandlimited intensity-modulation direct-detection channel is proposed. A new time-varying bias signal is added to the transmitted signal to make it nonnegative and provide a more power-efficient transmission than the previously considered constant bias. To exploit the benefits of the new signaling method, Nyquist and root-Nyquist pulses suitable for the use with this kind of bias are designed using two different methods. In the first method, new pulses are obtained by adding Nyquist pulses in the time domain with different combining coefficients, whereas in the second method, the pulses are obtained by the design of their frequency response. Analytical expressions for the asymptotic optical power efficiency and symbol error rate of the proposed schemes are derived and evaluated. At a spectral efficiency of 1 b/s/Hz, using on-off keying modulation and the proposed bias signal and pulses, up to 0.628 dB gains in asymptotic power efficiency can be achieved compared to the previously best known signaling scheme, which is based on squared sinc pulse shaping.