  We consider discrete Schr\"odinger operators with Sturmian potentials and
study the transport exponents associated with them. Under suitable assumptions
on the frequency, we establish upper and lower bounds for the upper transport
exponents. As an application of these bounds, we identify the large coupling
asymptotics of the upper transport exponents for frequencies of constant type.
We also bound the large coupling asymptotics uniformly from above for
Lebesgue-typical frequency. A particular consequence of these results is that
for most frequencies of constant type, transport is faster than for Lebesgue
almost every frequency. We also show quasi-ballistic transport for all coupling
constants, generic frequencies, and suitable phases.
