Choosing an appropriate proportion between debt and equity is one of the most important decisions in a financial management. 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 the bonds from the American market between 2002-2013. The financial sector companies were excluded from the sample due to a different financial statement structure and different motives of the hybrid debt issuance. Using the regression trees analysis, we give some hints, what is the main goal of the paper, for the optimal convertible debt financing, considering the most important characteristics of the issuers' financial standing and the parameters of issued convertibles. Our research let us to formulate a few conclusions. Firstly, we find some relationships between a conversion premium, a conversion period and a conversion ratio. Secondly, it turns out that most of the issuer's financial characteristics were not statistically significant for the issued convertibles. Finally, it was proved that a participation of fixed assets in a balance sheet seems to be one of the most important factors determining the internal structure of issued hybrid instruments which supports the assets substitution theory.