In traditional spread-spectrum techniques, a wideband transmit signal is obtained by modulating a wideband carrier by a narrowband signal containing a relatively low-rate message. In the receiver, the respective demodulation/despreading restores the information-carrying narrowband signal. In this paper, we introduce an alternative approach, where the low-rate information is encoded directly into a wideband waveform of a given bandwidth, without physical "spreading" of the carrier's frequency. The main advantages of this approach lie in extended options for encoding the information, and in retaining a reversible control over the temporal and amplitude structures of the modulating wideband waveforms. Significant "excess bandwidth" (over that needed to carry the information) enables us to use allpass filters to manage statistical properties and time-domain appearances of these waveforms without changing their spectral composition. For example, a mixture of transmitted waveforms can be shaped as a low-crest-factor signal (e.g. to reduce the burden on the power amplifier), and/or made statistically indistinguishable from Gaussian noise (e.g. for covert transmissions and physical layer steganography), while the selected components of the received waveform can be transformed into high-crest-factor pulse trains suitable for multiplexing and/or low-SNR communications. Further, control over the temporal and amplitude structures of wideband waveforms carrying low-rate information enables effective use of nonlinear filtering techniques. Such techniques can be employed for robust real-time asynchronous extraction of the information, as well as for separation of wideband signal components with identical spectral content from each other. This can facilitate development of a large variety of low-SNR and covert communication configurations.