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Physical studies of asteroids depend on an availability of lightcurve data. Targets that are easy to observe and analyse naturally have more data available, so their synodic periods are confirmed from multiple sources. Also, thanks to availability of data from a number of apparitions, their spin and shape models can often be obtained, with a precise value of sidereal period and spin axis coordinates. Almost half of bright ( H ≤ 11 mag ) main-belt asteroid population with known lightcurve parameters have rotation periods considered long ( P ≥ 12 h ) and are rarely chosen for photometric observations. There is a similar selection effect against asteroids with low lightcurve amplitudes ( a max ≤ 0.25 mag ). As a result such targets, though numerous in this brightness range, are underrepresented in the sample of spin and shape modelled asteroids. In the range of fainter targets such effects are stronger. These selection effects can influence what is now known about asteroid spin vs. size distribution, on asteroid internal structure and densities and on spatial orientation of asteroid spin axes. To reduce both biases at the same time, we started a photometric survey of a substantial sample of those bright main-belt asteroids that displayed both features: periods longer than 12 h, and amplitudes that did not exceed 0.25 magnitude. First we aim at finding synodic periods of rotation, and after a few observed apparitions, obtaining spin and shape models of the studied targets. As an initial result of our survey we found that a quarter of the studied sample (8 out of 34 targets) have rotation periods different from those widely accepted. We publish here these newly found period values with the lightcurves. The size/frequency plot might in reality look different in the long-period range. Further studies of asteroid spins, shapes, and structure should take into account serious biases that are present in the parameters available today. Photometric studies should concentrate on such difficult targets to remove the biases and to complete the sample. [ABSTRACT FROM AUTHOR]