The effect of annealing both in the oxygen atmosphere and at room temperatures on physical properties such as the pseudogap (Δ*(T)) and excess conductivity (σ΄(T)) of untwined YBa2Cu3O7-δ (YBCO) single crystal with a small deviation from oxygen stoichiometry is studied. It was revealed that as the charge carrier density, nf, increases, Тс also slightly increases, whereas the temperature of the pseudogap opening, T*, decreases noticeably, which is consistent with the phase diagram (PD) of cuprates. The excess conductivity in the vicinity of Tc is represented by the Aslamazov-Larkin and Hikami-Larkin fluctuation theories, illustrating the three-dimensional to two-dimensional (i.e. 3D-2D) crossover with an increase in temperature. The crossover temperature T0 determines the coherence length, which in the c axis is ξc(0) = 0.86 Å, that is 2.6 times larger than for optimally doped YBCO single crystals with defects. Taking into account the short coherence length in high-temperature superconductors, in the model of free charge carriers the phase relaxation time of fluctuating Cooper pairs is determined, τφ (100 K)= (4.55 ± 0.4) ·10-13 s, which is slightly (1.2 times) larger than in well-structured YBCO films, and as in films, does not depend on nf. It is shown that Δ*(T) at different annealing stages practically does not change its shape. As in the well-structured YBCO films, Δ*(T) demonstrates maximum at Tpair~ 124 K which depends weakly on nf. However, the maximum value of Δ*(Tpair) increases with increasing nf, as it follows from the PD of cuprates. Comparing the experimental data with the Peters-Bauer theory we estimated the density of local pairs <n↑n↓> ≈ 0.3 near Tc that is a common value for high-temperature superconductors.