Magnetic Resonance Imaging opens an alternative way to analyze wood structures using a non-destructive technology. It provides high resolution, compound-based contrast manipulation and increased data acquisition flexibility. The technique is particularly useful for tree logs, since they present several characteristics that can be used to reduce the long scan time. This study proposes a method that takes advantage of the log cylindrical symmetry, acquiring transverse 1-D projections with a helical and undersampled pattern. Linear interpolation is used to estimate the skipped data and slice images are reconstructed by filtered backprojection. The sequence is improved using selective multi-pass scanning, without major variations of the scan time. Computer simulations and experimental results show that the proposed technique can increase the scan speed by a factor of 6, while maintaining the ability to identify typical tree log characteristics.