We investigate a series of two-alternative forced-choice (2AFC) discrimination tasks based on malignant features of abnormalities in low-dose lung CT scans. A total of 3 tasks are evaluated, and these consist of a size-discrimination task, a boundary-sharpness task, and an irregular-interior task. Target and alternative signal profiles for these tasks are modulated by one of two system transfer functions and embedded in ramp-spectrum noise that has been apodized for noise control in one of 4 different ways. This gives the resulting images statistical properties that are related to weak ground glass lesions in axial slices of low-dose lung CT images. We investigate observer performance in these tasks using a combination of statistical efficiency and classification images. We report results of 24 2AFC experiments involving the three tasks. A staircase procedure is used to find the approximate 80% correct discrimination threshold in each task, with a subsequent set of 2,000 trials at this threshold. These data are used to estimate statistical efficiency with respect to the ideal observer for each task, and to estimate the observer template using the classification-image methodology. We find efficiency varies between the different tasks with lowest efficiency in the boundary-sharpness task, and highest efficiency in the non-uniform interior task. All three tasks produce clearly visible patterns of positive and negative weighting in the classification images. The spatial frequency plots of classification images show how apodization results in larger weights at higher spatial frequencies.