The interaction between the patient's expected outcome of an intervention and the inherent effects of that intervention can have extraordinary effects. Thus in clinical trials an effort is made to conceal the nature of the administered intervention from the participants in the trial i.e. to blind it. Yet, in practice perfect blinding is impossible to ensure or even verify. The current standard is follow up the trial with an auxiliary questionnaire, which allows trial participants to express their belief concerning the assigned intervention and which is used to compute a measure of the extent of blinding in the trial. If the estimated extent of blinding exceeds a threshold the trial is deemed sufficiently blinded; otherwise, the trial is deemed to have failed. In this paper we make several important contributions. Firstly, we identify a series of fundamental problems of the aforesaid practice and discuss them in context of the most commonly used blinding measures. Secondly, motivated by the highlighted problems, we formulate a novel method for handling imperfectly blinded trials. We too adopt a post-trial feedback questionnaire but interpret the collected data using an original approach, fundamentally different from those previously proposed. Unlike previous approaches, ours is void of any ad hoc free parameters, is robust to small changes in auxiliary data and is not predicated on any strong assumptions used to interpret participants' feedback.