The influence of hydrostatic pressure P up to 1.05 GPa on resistivity ρ , excess conductivity σ′(T) and pseudogap Δ⁎(T) is investigated in slightly doped single crystals of YBa2Cu3O7−δ ( and δ≈0.5). The critical temperature Tc is found to increase with increasing pressure at a rate , while decreases at a rate . Near Tc, independently on pressure, σ′(T) is well described by the Aslamasov–Larkin and Hikami–Larkin fluctuation theories, demonstrating a 3D–2D crossover with increase of temperature. The crossover temperature T0 determines the coherence length along the c -axis at P=0, which is found to decrease with increasing P . At the same time, Δ⁎ and the BCS ratio both increase with increasing hydrostatic pressure at a rate , implying an increase of the coupling strength with increasing P. At low temperatures below Tpair, the shape of the Δ⁎(T) curve is found to be almost independent of pressure. At high temperatures, the shape of the Δ⁎(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.