  We give a recursive formula for purely real Welschinger invariants of the
following real Del Pezzo surfaces: the projective plane blown up at $q$ real
and $s \leq 1$ pairs of conjugate imaginary points, where $q+2s\le 5$, and the
real quadric blown up at $s \leq 1$ pairs of conjugate imaginary points and
having non-empty real part. The formula is similar to Vakil's recursive formula
for Gromov-Witten invariants of these surfaces and generalizes our recursive
formula for purely real Welschinger invariants of real toric Del Pezzo
surfaces. As a consequence, we prove the positivity of the Welschinger
invariants under consideration and their logarithmic asymptotic equivalence to
genus zero Gromov-Witten invariants.
