  We present consistently ordered calculations of the structure functions
F_2(x,Q^2) and F_L(x,Q^2), in different expansion schemes. After discussing the
standard expansion in powers of alpha_s(Q^2) we consider a leading-order
expansion in ln(1/x) and finally an expansion which is leading order in both
ln(1/x) and alpha_s(Q^2), and which is the only really correct expansion
scheme. Ordering the calculation in a renormalization-scheme-consistent manner,
there is no factorization scheme dependence, and the calculational method
naturally includes to the ``physical anomalous dimensions'' of Catani. However,
it imposes stronger constraints than just the use of these effective anomalous
dimensions. A relationship between the small-x forms of the inputs F_2(x,Q_I^2)
and F_L(x,Q_I^2) is predicted. Analysis of a wide range of data for F_2(x,Q^2)
is performed, and a very good global fit obtained, particularly for data at
small x. The fit allows a prediction for F_L(x,Q^2) to be produced, which is
smaller than those produced by the usual NLO-in-alpha_s(Q^2) fits to F_2(x,Q^2)
and different in shape.
