  We employ realistic constraints on selection effects to model the Gamma-Ray
Burst (GRB) redshift distribution using {\it Swift} triggered redshift samples
acquired from optical afterglows and the TOUGH survey. Models for the Malmquist
bias, redshift desert, and the fraction of afterglows missing because of host
galaxy dust extinction, are used to show how the "true" GRB redshift
distribution is distorted to its presently observed biased distribution. Our
analysis, which accounts for the missing fraction of redshifts in the two data
subsets, shows that a combination of selection effects (both instrumental and
astrophysical) can describe the observed GRB redshift distribution. The
observed distribution supports the case for dust extinction as the dominant
astrophysical selection effect that shapes the redshift distribution.
