Until recently the B (b(1)Sigma(+)(g) (nu=1)-X-3 Sigma(-)(g) (nu=0)) and gamma (b(1)Sigma(+)(g) (nu=2)-X-3 Sigma(-)(g) (nu=0)) bands of oxygen in the visible region had not been used extensively in satellite remote sensing of the atmosphere. These bands roughly cover the regions around 14,527 and 15,904 cm(-1), respectively (0.69 and 0.63 mu m). However, these bands (in particular the B-band) are now being increasingly considered for future satellite missions. In this light, it is important to make sure that the reference spectroscopic parameters allow accurate retrieval of important physical characteristics from the atmospheric spectra. The spectroscopic parameters currently given for these bands in the HITRAN2008 spectroscopic database were tested against high-resolution atmospheric spectra measured with solar-pointing Fourier transform spectrometers at Park Falls, Wisconsin (B-band) and Kitt Peak, Arizona (gamma-band). It was found that the current HITRAN parameters cannot produce satisfactory fits of the observed spectra. In order to improve the database we have collected the best available measured line positions that involve the b(1)E(g)(+) (nu=1 and nu=2) states for the three most abundant isotopologues of oxygen and performed a combined fit to obtain a consistent set of spectroscopic constants. These constants were then used to calculate the line positions. A careful review of the available intensity and line-shape measurements was also carried out, and new parameters were derived based on that review. In particular, line shift parameters, that were not previously available, were introduced. The new data have been validated using the high-resolution atmospheric spectra measured with the Fourier transform spectrometers at Park Falls, Wisconsin (B-band) and Kitt Peak, Arizona (gamma-band) and have yielded substantial improvement. In addition, we report the first direct observation and analysis of the (OO)-O-16-O-18 lines in the gamma-band. (C) 2011 Elsevier Ltd. All rights reserved.