Feature search for a light bar with one orientation (or color) embedded in an array of bars with a very different orientation (or color) is quick, easy and independent of the number of array elements. In contrast, search for a conjunction target has a linear response time dependence on the number of distractors. Training can improve performance of both these tasks. We report that these properties may not be valid for eccentric stimulus presentation. In general, the two hemifields are not equally suited to search, and training is most effective in the weaker hemifield. In addition, the feature-search independence of set-size may not always be valid for stimulus arrays that are presented peripherally. Subjects were tested on orientation and color feature tasks, and on orientation-color conjunction search with 3 array sizes presented at fixation or eccentrically in the right or left hemifield. During a second testing session, improvement was so much greater for the non-preferred hemifield that sometimes the preference was switched. Surprisingly, preferred hemifield performance actually declined for some subjects. Thus, the hemifield preference effect seems related to competition, and perhaps an automatic attention-directing mechanism. We confirmed the central presentation set-size independence for feature search but found a great difference between large and small arrays when presentation was lateral. There are two sources of this array size effect: 1. Target eccentricity, demonstrated by comparing performance for different target locations with the same array size. 2. Target location uncertainty, seen by comparing performance for different size arrays when the target elements appeared at the same locations. Training also affected the array-size dependence, changing search performance from set-size dependent to independent or vice versa at the point of greatest training effect.