Ought we to sentence people to psychiatric treatment?

In principle, there seem to be three main ways in which society can react when people commit crimes under influence of mental illness. (1) The standard model. We excuse them. If they are dangerous they are detained in the interest of safety of the rest of the citizens. (2) The Swedish model. We hold them responsible for their criminal offence, we convict them, but we do not sentence them to jail. Instead, we sentence them to psychiatric treatment. (3) My model. We sentence them to jail, but offer them (voluntary) psychiatric treatment. The advantages of my model are obvious. We get a clear delineation of roles. We allow the psychiatrist to be just a doctor, not a warden. We liberate psychiatry of the objective of deciding whether people who were mentally ill when they committed criminal offences 'could have acted otherwise' -- a hopeless task. We allow that psychiatrists live up to their professional ethical code (The Hawaii Declaration). We treat psychically ill persons as 'normal', we allow them to repent their crimes, which renders easier their recovery. However, two objections to my model come to mind. First of all, is it not unfair to sentence people to jail who could not help doing what they did? And, secondly, the question of fairness set to one side, is it not inhumane to sentence mentally ill persons to jail? Is it not inhumane to the mentally ill persons themselves, and does it not mean that they will be a burden to other prisoners? In my paper I show that, if our system of criminal punishment takes a civilised form, neither of these objections carries any weight.