This paper proposes a technique for using control relevant criteria in H-infinity identification, The work reported here has its background in a desire to understand the closed-loop versus open-loop issue in control relevant identification as highlighted in the IEEE TRANSACTIONS ON AUTOMATIC CONTROL special issue technical note [17]. The proposed technique has some features in common with the iterative closed-loop Schrama scheme but is constructed so as to be able to obtain control relevant reduced complexity models also directly from open-loop data (for stable systems). It is demonstrated that the proposed technique solves, with the initial open-loop data only, the examples [17]-[20] earlier treated in the literature using the iterative closed-loop Schrama scheme.