The first covenant in the Bible (after the Flood) expresses the self-restraint God will exercise in punishing Mankind. The second covenant is the Covenant of the Parts. The third is the covenant of circumcision. That covenant is also a covenant of self-restraint.
To circumcize the zakhar is a symbol of effeminating the male. It is an indication of semiconduction. The hole of the female, the neqeiva, and the protrusion of the male, the zakhar, are mediated by the circumcized zakhar which is neither castrated nor trans-gendered into femaleness but is moderated by the restraint that is implied in the act of circumcision and in the submission to a higher authority implied by it. The brit milah is an act of subjegation that mirrors the act of self-restraint as symbolized by the brit qeshet of Noah. These are the three covenants of Genesis.
The corresponding covenants of Exodus are also three-fold: the qeshet of the paschal lamb; the brit Sinai , couple with the second brit at Sinai which is embodied in the mishkan (here God is the One Who circumcizes Himself, as it were, by contracting Himself into the space of the mishkan); and the brit Moav.
Neither the paschal covenant nor the covenant of the mishkan are denominated explicitly as brit but they are defined by chuqim, which are the operational manifestations of covenant.