A convertible bond may be an attractive financial instrument that helps to achieve the optimal capital structure of a company. In this paper, we analyze 562 issues of bonds from the American market between 2002 and 2013. Using regression trees analysis, we give some hints with respect to the design of convertible debt financing, which is the main goal of the paper, considering the most important characteristics of the issuers’ financial standing and the parameters of issued convertibles. Our research let us formulate a few conclusions. Firstly, we identified some relationships between a conversion premium, a conversion period and a conversion ratio applied by issuers. Secondly, it turned out that most of the issuer’s financial characteristics were not statistically significant for the issued convertibles. Finally, we found out that the share of fixed assets in the balance sheet amount seems to be one of the most important factors determining the internal structure of issued hybrid instruments, which supports the assets substitution theory.