The influence of hydrostatic pressure up to P=1.05 GPa on resistivity, excess conductivity σ ′ (T ) and pseudogap ∆ * (T ) is investigated in slightly doped single crystals of Y Ba2Cu3O 7−δ (Tc(P = 0) ≈49.2 K and δ ≈ 0.5). The critical temperature Tc is found to increase with increasing pressure at a rate dTc/dP = +5.1 KGP a −1 , while ρ(300) K decreases at a rate dlnρ/dP = (−19±0.2)% GP a −1 . Near Tc, independently on pressure, the σ ′ (T ) is well described by the Aslamasov-Larkin and HikamiLarkin fluctuation theories, demonstrating a 3D-2D crossover with increase of temperature. The crossover temperature T0 determines the coherence length along the c-axis ξc(0) ≃ (3.43 ± 0.01)Å at P=0, which is found to decrease with increasing P. At the same time, ∆ * and the BCS ratio 2∆ * /kB Tc both increase with increasing hydrostatic pressure at a rate dln∆ * /dP ≈ 0.36 GP a −1 , implying an increase of the coupling strength with increasing P. At low temperatures below Tpair, the shape of the ∆ * (T ) curve is found to be almost independent on pressure. At high temperatures, the shape of the ∆ * (T ) curve changes noticeably with increasing P, suggesting a strong influence of pressure on the lattice dynamics. This unusual behavior is observed for the first time.