Restriction enzymes are the bread and butter of Molecular Biology. Nonetheless, how restriction enzymes recognize and cleave their target is not always clear. When developing a method for the enzymatic production of oligonucleotides, we noticed that type II endonucleases BtsCI and BseGI, which recognize the sequence GGATGNN^, perform incomplete digestions of DNA hairpins, with the top strand nick not always occurring correctly. We tested the cutting of synthetic hairpins containing all possible combinations of dinucleotides following the recognition site and our results show that all sequences containing one adenine following GGATG were digested more efficiently. We further show that the same sequence preference is also observable in double stranded DNA at higher Mg2+ concentrations and even in optimal conditions. Kinetic results show that BtsCI has a noteworthy difference in the first-rate constants between different sequences and between the two catalytic domains. An increase in Mg2+ resulted in a drastic decrease in the catalytic activity of the top (sense) strand that wasn't always accompanied by a nick in the bottom strand (antisense).