How many phases meet at the chiral critical point?

We explore the phase diagram of Nambu-Jona-Lasinio-type models near the chiral critical point allowing for phases with spatially inhomogeneous chiral condensates. In the chiral limit it turns out that the region in the mean-field phase diagram where those phases are energetically preferred very generically reaches out to the chiral critical point. The preferred inhomogeneous ground state in this vicinity possibly resembles a lattice of domain wall solitons. This raises the question of their relevance for the phase diagram of QCD.