  A ``3D'' Mathematica@-generated picture of monopoles and Dirac strings in
$D=2+1$ compact QED is given. In the Villain approximation, the monopole part
of the partition function factorizes from the Dirac string part, which
generates the photon propagator. Numerical experiments in exact compact QED
confirm this result: photon mass pole $M_\gamma$, originally nonzero, is
insensitive to monopole prohibition but almost vanishes if Dirac strings are
prohibited.
