An essential task in comparative genomics is usually to de- compose two or more genomes into synteny blocks, that is, segments of chromosomes with similar contents. In this paper, we study the Maxi- mal Strip Recovery problem (MSR) [Zheng et al. 07], which aims at nding an optimal decomposition of a set of genomes into synteny blocks, amidst possible noise and ambiguities. We present a panel of new or im- proved FPT and approximation algorithms for the MSR problem and its variants. Our main results include the rst FPT algorithm for the vari- ant -gap-MSR-d, an FPT algorithm for CMSR-d and -gap-CMSR-d running in time O(2:360kpoly(nd)), where k is the number of markers or genes considered as erroneous, and a (d + 1:5)-approximation algorithm for CMSR-d and -gap-CMSR-d.