In the context of protein engineering, we consider the problem of computing an mRNA sequence of maximal codon-wise similarity to a given mRNA (and consequently, to a given protein) that additionally satisfies some secondary structure constraints, the so-called MRSO problem . Since the MRSO problem is known to be
-hard , Bongartz proposed in  to attack the problem using the concept of parameterized complexity. In this paper we follow this suggested approach by devising fixed-parameter algorithms for several interesting parameters of MRSO. We believe these algorithms to be relevant for practical applications today, as well as for several future applications. Furthermore, our results extend the known tractability borderline of MRSO, and provide new research horizons for further improvements of this sort.