P elements, both complete and incomplete, contain a left and right end, normally depicted as pointing away from each other. Here, we examine the properties of P elements that may be described as 're-arranged elements' or 'inside-out elements', containing inverted ends. Two such structures exist, having either ends pointing towards each other, 'headto-head or H-H', or ends pointing in the same direction 'head-to-tail or H-T'. We show that both structures are unstable in the presence of P element transposase. For the H-H element there is a high frequency of deletion of the intervening material and almost exact rejoining of element ends with the 4 bp CATG palindromic end sequence shared by the two element ends. This result is predicted by the Beall and Rio model of P element excision. For the H-T element there is a high frequency of exact excision of the entire inverted right-end, a result again predicted by the Beall and Rio model. Both structures lead to recombination in the way expected from a normal element. The rates of recombination are, however, much lower than might be expected from the organization of ends, a result that can be explained in terms of the low likelihood of insertion into a chromosomal region lacking another P element end. We also investigate the properties of combinations of re-arranged and normal elements, and show that there is a directionality property when left and right ends are combined in trans that can be explained in terms of strand repair.