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I am trying to pay more attention to the pattern of veins in the wings. I can't recall seeing a fly with such straight veins?and few of them.

ID help appreciated.

Found in a damp woodland near the Ohio River, West Virginia, USA, 13 June 2006.

My recollection is that the overall length was circa 3.33 mm, but I am not certain about this.

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Hi Stephen.
Yes, simple venation, Dolichopodidae.
Nikita

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This is barely a guess, but the fly may be a female of genus Diaphorus (Dolichopodidae).

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Why not Chrysotus?

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Just so I can learn more about how to identify fly familes, what characteristics make this fly a member of Dolichopodidae?

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Well, I'm not saying it isn't, but

a) The 3rd segment appears to be very short, not larger than previous segments. Admittably they are out-of-focus and perhaps they are damaged and the postpedicel is missing.
b) >3 mm is rather large for a Chrysotus (at least in Europe) but a perfectly normal size for Diaphorus.
c) It does not feel like a Chrysotus. Don't ask why;)

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A small fly with metallic green color (obscured by pollinosity to a varying degree) is a prime candidate for a Doli. Similar color is found in few other familes, mostly on very small, pudgy flies (Melagromyza in Agromyzidae, Psilopa in Ephydridae and others) - and of course on bluebottles and greenbottles;)

The simple wing venation is shared by all classical Dolies; just four long major veins (two radial veins, one medial, one cubital) and one crossvein (m-cu) in the outer part of the wing. Technically dolies have also the 'r-m' crossvein, but it is near the base of wing, not in the middle as in most other flies. So practically dolies have only one major crossvein. Some dolies are not metallic but yellow; for them the wing venation is the primary reference point.

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In Russian Dolichopodidae - Zelenushki, which may be translated as small greenish flies;)