  The excess adsorption $\Gamma $ in two-dimensional Ising strips $(\infty
\times L)$ subject to identical boundary fields, at both one-dimensional
surfaces decaying in the orthogonal direction $j$ as $-h_1j^{-p}$, is studied
for various values of $p$ and along various thermodynamic paths below the
critical point by means of the density-matrix renormalization-group method. The
crossover behavior between the complete wetting and critical adsorption
regimes, occurring in semi-infinite systems, are strongly influenced by
confinement effects. Along isotherms $T=const$ the asymptotic power law
dependences on the external bulk field, which characterize these two regimes,
are undercut by capillary condensation. Along the pseudo first-order phase
coexistence line of the strips, which varies with temperature, we find a broad
crossover regime where both the thickness of the wetting film and $\Gamma$
increase as function of the reduced temperature $\tau$ but do not follow any
power law. Above the wetting temperature the order parameter profiles are not
slab-like but exhibit wide interfacial variations and pronounced tails. Inter
alia, our explicit calculations demonstrate that, contrary to opposite claims
by Kroll and Lipowsky [Phys. Rev. B {\bf 28}, 5273 (1983)], for $p=2$ critical
wetting transitions do exist and we determine the corresponding wetting phase
diagram in the $(h_1,T)$ plane.
