  We study a d-wave superconductor with dominant $d_{x^2-y^2}$-wave order
parameter and subdominant pairing in either the $s$- or the $d_{xy}$-wave
channel near a surface. In particular we analyze the influence of surface
roughness on the mixed order parameter which may break the time-reversal
symmetry. We find that the subdominant component is suppressed by the roughness
independent of its pairing symmetry; for very rough surfaces the subdominant
component may even vanish completely. Additionally we discuss a possible
real-valued admixture which counteracts the suppression of the
$d_{x^2-y^2}$-wave order parameter at the surface.
