This paper address the problem of classification of BPSK-modulated multicarrier signals with the peak-to-average power ratio (PAPR) exceeding 3/4 of the maximal possible value. By providing a simple characterization of such signals, an upper bound on their number are derived and propose a simple sufficient condition for the signals to have low PAPR. Based on this, a simple method for generation of signals with guaranteed PAPR gain of more than 2.5 dB using only two redundant tones are described.