In the last decade, a manifold of studies has been conducted to elucidate the compensation mechanism in strain relaxed N-doped ZnSe layers of about 1 mu m or more thickness. It has mostly been disregarded, however, that in optoelectronic devices often N-doped layers thinner than the critical thickness are used. We have investigated the donor-acceptor-pair (DAP) recombination in N-doped MBE-grown ZnSe layers being as thin as 100, 20, 10, and 5 nm embedded in undoped ZnMgSSe barriers lattice matched to the GaAs substrates. The temperature and intensity dependence of the DAP recombination as well as the observation of two-hole transitions of the nitrogen acceptor on the Se site leads us to the conclusion that a not-yet investigated very shallow donor is involved in the DAP recombination. This impurity with a thermal activation energy of 19 +/- 1 meV seems to be the dominant compensating donor in ultrathin fully-strained N-doped ZnSe, at least if embedded in quaternary barriers.