In the work it is discussed about one of the three possible agreements between the prosecutor and the defendant, agreement on testifying by a convicted, where a new institute is pointed out, taken from Anglo-Saxon law, representing a specific way of acquiring a 'cooperative' witness. After the introductory part, concluding an agreement is explained in detail, i. e. who and under which circumstances can conclude an agreement, and who cannot, with stating that it would be good to prolong the compulsory defense until the moment of making a decision about request for punishment mitigation. Then the contents of the agreement on testifying by a convicted is pointed out and it is specified who decides about it, stating which decisions are made and for which reasons. A special attention is given to questioning a cooperating convicted person and a proven value of his statement, with a warning that the court must be particularly careful when evaluating the statement because a greater danger of false statement exists. This danger is present because the cooperating convicted person will get an expected privilege as a mitigated punishment only if the trial where he testified ended with a final conviction, which makes him a witness especially interested in the outcome of the trial and therefore potentially unreliable. In the part of work related to the connection of the court to the decision about accepting the agreement, a number of legally technical and formal shortcomings about legal solutions are pointed out. It is, for example, stated that the legislator prescribes that the solution about accepting the agreement on testifying by a convicted obliges the court when making a decision about a criminal sanction in a repeated procedure (regulated by act 470-481), and it is not referred to that procedure at all, but to the procedure for punishment mitigation (regulated by act 557-561). Also the attention is drawn to the actual and potential problems in practice stating the ways the noticed problems could be solved. One of the problems noticed is in the fact that the procedure for punishment mitigation is initiated within 30 days from the final conviction brought in the procedure where the cooperating convicted person testified. As there is a possibility that the cooperating convicted person had served the whole sentence or most of its part by then, he could, for that reason, be left without the privilege of punishment mitigation, therefore it is suggested that Law on the Execution of criminal Sanctions is changed in a way that the cooperating convicted person would be given an opportunity to postpone or interrupt serving of punishment until the procedure where he testified is validly completed. The last part of the work contains conclusive considerations where it is ascertained the justification of this institute, pointing out that its application is rather limited, after which the way the noticed problems could be solved is emphasized, with the aim of improved and more efficient application.