  Rational pairs, recently introduced by Koll\'ar and Kov\'acs, generalize
rational singularities to pairs $(X,D)$. Here $X$ is a normal variety and $D$
is a reduced divisor on $X$. Integral to the definition of a rational pair is
the notion of a thrifty resolution, also defined by Koll\'ar and Kov\'acs, and
in order to work with rational pairs it is often necessary to know whether a
given resolution is thrifty. In this paper we present several foundational
results that are helpful for identifying thrifty resolutions and analyzing
their behavior. We also show that general hyperplane sections of rational pairs
are again rational.
  In 1978, Elkik proved that rational singularities are deformation invariant.
Our main result is an analogue of this theorem for rational pairs: given a flat
family $X\to S$ and a Cartier divisor $D$ on $X$, if the fibers over a smooth
point $s\in S$ form a rational pair, then $(X,D)$ is also rational near the
fiber $X_s$.
