Upper limits on the extinction-corrected optical fluxes of PSR  J1357−6429 (left) and PSR  J1048−5832 (right) compared with the low-energy extrapolations of the X-ray (solid black) and γ-ray (solid blue) spectral models that best fit the XMM-Newton, Chandra (Esposito et al. 2007; Marelli et al. 2011), and Fermi (Lemoine-Goumard et al. 2011; Abdo et al. 2009) data. The plotted optical flux upper limits are corrected for interstellar extinction based upon the best-fit value of the N_H. The dotted lines in the left panel correspond to the PL and BB components to the model X-ray spectrum. In both panels, the yellow and blue-shaded areas (left to right) indicate the 1σ uncertainty on the extrapolations of the X and γ-ray PLs, respectively. The vertical red dashed lines mark the uncertainty on the extinction-corrected optical flux upper limits, computed around the best-fit value of the N_H. For PSR  J1357−6429, we neglected the uncertainties on the extrapolation of the BB component, whose contribution in the optical band is negligible.