Filter bank-based multicarrier (FBMC) systems based on offset quadrature amplitude modulation (FBMC/OQAM) have recently attracted increased interest (in applications including DVB-T, cognitive radio, and powerline communications) due to their enhanced flexibility, higher spectral efficiency, and better spectral containment compared to conventional OFDM. FBMC/OQAM suffers, however, from an imaginary inter-carrier/inter-symbol interference that complicates signal processing tasks such as channel estimation. Most of the methods reported thus far in the literature rely on the assumption of (almost) flat subchannels to more easily tackle this problem, with the aim of addressing it in a way similar to OFDM. However, this assumption may be often quite inaccurate, due to the high frequency selectivity of the channel and/or the small number of subcarriers employed to cope with frequency dispersion in fast fading environments. In such cases, severe error floors are exhibited at medium to high signal-to-noise ratio (SNR) values, that cancel the advantage of this modulation over OFDM. Moreover, the existing methods provide estimates of the subchannel responses, most commonly in the frequency domain. The goal of this paper is to revisit this problem through an alternative formulation that focuses on the estimation of the channel impulse response itself and makes no assumption on the degree of frequency selectivity of the subchannels. The possible gains in estimation performance offered by such an approach are investigated through the design of optimal (in the mean squared error sense) preambles, of both the full and sparse types, and of the smallest possible duration of only one pilot FBMC symbol. Existing preamble designs for flat subchannels are then shown to result as special cases. The case of longer preambles, consisting of two consecutive pilot FBMC symbols, is also analyzed. Simulation results are presented, for both mildly and highly frequency selective channels, that demonstrate the significant improvements in performance offered by the proposed approach over both OFDM and the optimal flat subchannel-based FBMC/OQAM method. Most notably, no error floors appear anymore over a quite wide range of SNR values.