  We investigate the energy behavior of the diffraction cone in the exclusive
vector meson production in diffractive DIS within the k_t-factorization
approach. In our calculations, we make full use of fits to the unintegrated
gluon structure functions extracted recently from experimental data on F_2p.
Confirming early predictions, we observe that shrinkage of the diffraction cone
due to the slope of the Pomeron trajectory is significantly compensated by the
anti-shrinkage behavior of the gamma -> V transition. In order to match recent
ZEUS data on the energy behavior of the diffraction slope,
alpha^prime_eff(J/psi, exp.) = 0.115 +/- 0.018 (stat.) +0.008-0.015(syst.)
GeV^-2, we had to use an input value alpha^\prime_Pomeron = 0.25 GeV^-2. We
investigate the compensation effect in detail and give predictions for
Q^2-dependence of the rate of cone shrinkage for different vector mesons.
