In a tennis match it is not uncommon for games to ‘go with service’ (ie. 1-0, 1-1, 2-1, 2-2, 3-2, so on). When this occurs, the player who serves first is either ahead by one game, or the games’ score is equal. Some commentators, players, argue that the person who serves first has a psychological advantage in that his/her opponent is very often ‘playing catch-up’. Assuming that such a (non-zero) psychological advantage of ‘being ahead in the games’ score’ exists, the advantage of serving first in a set between two equal players, is determined. In the presence of such ‘front-runner’ psychological effects, alternative methods or rules for allocating service to the players are considered, and some are shown to be fairer than the present rule. A proposal consisting of two modifications to the present rules is put forward for consideration. One of these modifications is very easy to apply. The reverse psychological effect to the above, the ‘back-to-the-wall’ effect, occurs when a player performs better when behind. The proposal is seen to be fairer than the present method for the cases in which both players A has either a positive or negative psychological effect and player B also has an equivalent positive or negative effect. Further, the application of the proposal to doubles is also considered and a modification for doubles suggested for consideration.