Context. Classical chemical analyses may be affected by systematic errors that would cause observed abundance differences between dwarfs and giants. For some elements, however, the abundance difference could be real. Aims. We address the issue by observing 2 solar-type dwarfs in NGC 5822 and 3 in IC 4756, and comparing their composition with that of 3 giants in either of the aforementioned clusters. We determine iron abundance and stellar parameters of the dwarf stars, and the abundances of calcium, sodium, nickel, titanium, aluminium, chromium, silicon, and oxygen for both the giants and dwarfs. For the dwarfs, we also estimate the rotation velocities, and and lithium abundances. We improve the cluster parameter estimates (distance, age, and reddening) by comparing existing photometry with new isochrones. Methods. We acquired UVES high-resolution, of high signal-to-noise ratio (S /N) spectra. The width of the cross correlation profiles was used to measure rotation velocities. For abundance determinations, the standard equivalent width analysis was performed differentially with respect to the Sun. For lithium and oxygen, we derived abundances by comparing synthetic spectra with observed line features. Results. We find an iron abundance for dwarf stars equal to solar to within the margins of error for IC 4756, and slightly above for NGC 5822 ([Fe/H] = 0.01 and 0.05 dex respectively). The 3 stars in NGC 4756 have lithium abundances between Log N(Li) ≈ 2.6 and 2.8 dex, the two stars in NGC 5822 have Log N(Li) ≈ 2.8 and 2.5, respectively. Conclusions. For sodium, silicon, and titanium, we show that abundances of giants are significantly higher than those of the dwarfs of the same cluster (about 0.15, 0.15, and 0.35 dex). Other elements may also undergo enhancement, but all within 0.1 dex. Indications of much stronger enhancements can be found using literature data. But artifacts of the analysis may be partly responsible for this.