# Model complete theories of henselian local rings which are not nec valuation rings

I just want to ask if anybody as any examples of a first order model complete theorie of henselian local rings which is not some theory of valuation rings. More precisely-

I am looking for a theory $T$ of the language of rings such that

1. Every model of $T$ is a henselian local ring
2. There exists a model of $T$ that is not a valuation ring
3. $T$ is model complete.

Indeed, does anybody know anything about that model theory of henselian local rings?