Pneumatic (air-filled) postcranial bones

We see that the postcranial bones of pterosaurs, secondarily flightless maniraptors and birds are pneumatic.
Coelurosaur dinosaurs did not have pneumatic postcranial bones.

http://www.oucom.ohiou.edu/dbms-ocon...eumaticity.pdf

Pneumatic (air-filled) postcranial bones are unique to birds among extant tetrapods. Unambiguous skeletal correlates of postcranial pneumaticity first appeared in the Late Triassic (approximately 210 million years ago), when they evolved independently in several groups of bird-line archosaurs (ornithodirans). These include the theropod dinosaurs [maniraptors] (of which birds are extant representatives), the pterosaurs, and sauropodomorph dinosaurs. [Note that sauropodomorph dinosaurs are not claimed to be on the purported line leading to birds]. Increases in skeletal pneumaticity occurred independently in as many as 12 lineages, highlighting a remarkably high number of parallel acquisitions of a bird-like feature among non-avian theropods.  However, the body size threshold for extensive pneumatisation is lower in theropod lineages more closely related to birds (maniraptorans). Thus, relaxation of the relationship between body size and pneumatisation preceded the origin of birds and cannot be explained as an adaptation for flight. We hypothesise that skeletal density modulation in small, non-volant, maniraptorans resulted in energetic savings as part of a multi-system response to increased metabolic demands. Acquisition of extensive postcranial pneumaticity in small-bodied maniraptorans may indicate avian-like high-performance endothermy.

There are two possible explanations about how these maniraptors could be non-volant.

One is the way purported by the dino to bird theory (they are purported to be intermediate between dinosaur and Paraves). That fails because they came millions of years later.

The other is as secondarily flightless. And being secondarily flightless, they would have inherited their pneumaticity from their flying paravian ancestors. Their pneumaticity was to accommodate air sacs which is part of the unique breathing system that pterosaurs had and birds have.
So that explains the "postcranial pneumaticity in small-bodied maniraptorans". They evolved from flying paraves which had evolved from pterosaurs.

Also see:
http://pterosaurnet.blogspot.ca/2010/05/another-thing-to-watch-for.html
and
http://www.ucmp.berkeley.edu/science/profiles/wedel_0609.php
and
http://pterosaurnet.blogspot.ca/2011/11/breathing-pterosaurs-are-like-birds.html