In this paper the deformation of a translating fluid drop is examined in the limit of low Reynolds and capillary numbers. The general case of an arbitrarily varying interfacial tension is considered here. With the capillary number as a perturbation parameter, an expansion is carried out for small deformation to satisfy the normal stress condition. This leads to a rapidly converging Legendre series expansion for the deformation. This general result is applied to the special case of a translating drop with a stagnant cap of surfactant. An interesting feature of this special case is that although the shear stress at the interface has a square root singularity, the total normal stress is non-singular.