Preamble waveforms are commonly adopted to enable initial timing and frequency synchronization in most orthogonal frequency division multiplexing systems. To enable initial synchronization on both coarse and fine scales efficiently, these waveforms are constructed from appropriately designed preamble sequences, widely in conjunction with a special repetitive structure of the chosen sequence. The special structure is particularly facilitative to coarse synchronization while the preamble sequence itself affects fine synchronization essentially. Although performance optimality is not thoroughly established for all system setups and channel conditions, Zadoff-Chu and complex pseudorandom (PN) sequences, which possess, respectively, exact and near zero periodic autocorrelation (ZAC) properties, are extensively adopted to achieve robust synchronization while associating preamble waveforms with low peak to average power ratio (PAPR). Unfortunately, preamble waveforms carrying these sequences entail large power spectral sidelobes and are not spectrally compact. In this paper, new ZAC and near-ZAC sequences are developed to construct spectrally compact preamble waveforms adopting a repetitive or nonrepetitive structure. These sequences are shown to endow the corresponding preamble waveforms with high spectral compactness and low waveform PAPR while providing robust initial synchronization performance comparable to conventional ZAC sequences and superior to complex PN sequences.