Despite the popularity and importance of linear dispersion (LD) codes, precoding for LD codes has rarely been investigated. In this paper we propose a method for designing a precoder codebook for LD codes in spatially and temporally correlated channels. Our codebook consists of two parts: a unitary codebook and a diagonal codebook. We propose a systematic algorithm for a unitary code- book design because unitary codebooks are hard to generate using numerical optimization methods. For each column (starting with the first column), we generate a set of vectors in the null space of previous columns. These vectors are generated by skewing i.i.d. unit vector codebooks by means of channel statistics-dependent transformations. A diagonal codebook is generated using a vector quantization technique. We use mutual information as a design criterion throughout this paper. Numerical results illustrate the benefits of matching a codebook to channel statistics and employing adaptive power shaping.