We address the long-standing judicial debate over inquisitorial and adversarial procedures in criminal trials, focusing on the incentives to collect evidence of a defendant's guilt and innocence. We demonstrate three shortcomings of the former procedure: (i) a judge may suffer a trilemma or a quandary among three tasks she confronts, i.e., an incentive scheme to improve the performance of one task impairs the performance of one or two of the others; (ii) it underperforms the latter procedure in collecting evidence at cost if private interests in winning a suit are more motivating than the public interests in avoiding erroneous judgments; (iii) incentive arrangements are so constrained that it may be impossible to induce high efforts of investigation. However, the shortcoming (ii) might be negated when the private interests lead adversely to obscuring, rather than revealing evidence.