The estimation of the structural model poses a major challenge as its underlying asset (the firm's asset value) is not directly observable. We extend the maximum likelihood (ML) method of Duan (1994 and 2000), and propose a quasi-maximum likelihood (QML) approach that remains appropriate under alternative Markov assumptions, arbitrary debt payment schedules, and extended balance sheets. QML alternates between dynamic programming and maximum likelihood to simultaneously solve and estimate general structural settings. QML is highly flexible and effective. To support our construction, we conduct a numerical investigation and show that ML and QML agree in Merton's (1974) setting. Then, we achieve an empirical investigation, spotlight the credit-spread puzzle, and discuss a partial remedy via jumps and bankruptcy costs.