A perfectly acceptable construction

I think that the indefinite article is completely valid.

This is just an off-the-cuff comment, but I think it's an idiomatic issue. You can't quite put your finger on what's wrong because all of the versions you've asked about are grammatically correct. the problem with them is that they are somewhat awkward phrases that are not commonly used. Few would say "That house has a great construction." Rather, one would say "That house is well-constructed" or "That house is well-built" or "That is a well-built house." It's sort of like saying "My, you have had a great cutting of hair!" when most people would say, "Hey, that's a great haircut!" Both are grammatically correct, but the former sounds like you're an alien from another planet and learned English solely by monitoring old radio and TV broadcasts that have leaked through space across many light-years to your home world.

I don't think "a (adjective) construction" is an idiom just yet. The noun "construction" means the process, act, or manner of constructing – making – something. It can also be the thing constructed. To say that a house has "a great construction" is not incorrect: the reference is to the manner of construction. However, the phrasal form is trendy, and therefore apt to annoy.

In the case of "a durable cotton construction," we are nearing the realm of jargon. The garment industry uses the word "construction" to mean both the manner in which an article of clothing is made and the material it is made of. The latter is an irregular use of the word, but perfectly understood within the industry (and to anyone who watches Bravo). Unfortunately, it has also become part of ad-speak shorthand, suitable for the J C Penny catalog and not much more. You don't need to be Ambrose Bierce to be biased against it.

Hi Josh,

I'm with you! Although according to other commentators, those constructions are not grammatically incorrect, I have a problem with them, too. I think of the noun "construction" as the completed object. Therefore, we shouldn't say a T-shirt has a good construction; the T-shirt itself IS the good, completed construction. When I comment on a student's sentence structure, I write, "good sentence structure here!" I don't say "This sentence has a good construction." A completed house, T-shirt, or sentence is a completed thing, a complete construction, no longer a thing in progress. Therefore, we should refer to it as such, without the indefinite article or phrased better than the strange ways you listed as annoying (because they are!)