  It is known for linear operators with polynomial coefficients annihilating a
given D-finite function that there is a trade-off between order and degree.
Raising the order may give room for lowering the degree. The relationship
between order and degree is typically described by a hyperbola known as the
order-degree curve. In this paper, we add the height into the picture, i.e., a
measure for the size of the coefficients in the polynomial coefficients. For
certain situations, we derive relationships between order, degree, and height
that can be viewed as order-degree-height surfaces.
