Although we have seen that most of the MC signals have peaks of value about √n ln n, there are plenty of signals with maxima of order √n. This chapter is devoted to methods of constructing such signals. I begin with relating the maxima in signals to the distribution of their a periodic correlations (Theorem 7.2). Then I describe in Section 7.2 the Rudin–Shapiro sequences over {−1, 1}, guaranteeing a PMEPR of at most 2 for n being powers of 2. They appear in pairs, where each one of the sequences possesses the claimed property. The Rudin–Shapiro sequences are representatives of a much broader class of complementary sequences discussed in Section 7.3. The signals defined by these sequences also have a PMEPR not exceeding 2, while existing for a wider spectrum of lengths. In Section 7.4, I introduce complementary sets of sequences. The number of sequences in the sets can be more than two, and the corresponding sequences have a PMEPR not exceeding the number of sequences in the set. In Section 7.5, I generalize the earlier derived results to the polyphase case, and describe a general construction of complementary pairs and sets stemming from cosets of the first-order Reed–Muller codes within the second-order Reed–Muller codes. Another idea in constructing sequences with low PMEPR is to use vectors defined by evaluating the trace of a function over finite fields or rings. This topic is explored in Section 7.6 using estimates for exponential sums. Finally, in Sections 7.7 and 7.8, I study two classes of sequences, M-sequences and Legendre sequences, guaranteeing PMEPR of order at most (ln n)2.