The experimental lineshapes of the carboxyl and methyl carbon resonances of fully 13C enriched L-Alanine are studied in detail at different MAS frequencies and decoupling field strengths. Complex lineshapes at intermediate spinning speeds were explained by the joint effect of off rotational resonance and coherent CSA-dipolar cross-correlation. Whereas off rotational-resonance effects lead to complex lineshapes due to a splitting of some energy levels, coherent CSA-dipolar cross-correlation introduces either a differential intensity and/or a differential broadening of the lines of the J-multiplet. The conditions which lead to such effects are explained and experimentally verified. Additional simulations show that these effects can be expected over a wide range of static magnetic fields and are not restricted to L-Alanine.