  We revisit the calculation of one-loop corrections to the partition functions
of a string ending on a circular or straight line in type IIB string theory on
$AdS_3\times S^3 \times T^4$ supported by a mixture of 3-form fluxes depending
on a parameter $q$ (with $q=0$ being R-R and $q=1$ pure NS-NS cases).
Correcting earlier results in the literature, we find that the partition
function depends on $q$ only through rescaled tension $T= T_0/(1-q^2)$.
