  In this work, we consider Dirac-type operators with a constant delay less
than two-fifths of the interval and not less than one-third of the interval.
For our considered Dirac-type operators, an incomplete inverse spectral problem
is studied. Specifically, when two complex potentials are known a priori on a
certain subinterval, reconstruction of the two potentials on the entire
interval is studied from complete spectra of two boundary value problems with
one common boundary condition. The uniqueness of the solution of the inverse
problem is proved. A constructive method is developed for the solution of the
inverse problem.
