I've been having problems with these for quite some time now.
These are the targeted keywords:
- widget
- blue widget
- rectangle blue widget
So, I have multiple groups with specific ads:
- group widget (targeting 'widget' phrase/exact)
- group blue widget (targeting 'blue widget' phrase/exact)
- group rectangle blue widget (targeting 'rectangle blue widget' phrase/exact)
In theory, this means that when somebody searches for 'blue widget' the ad from group blue widget should show. And if someone searches for 'rectangle blue widget' the ad from group rectangle blue widget should appear.
In theory. In practice I open AdPreview Tool and see that for 'blue widget' the ad from group widget is showing.
Any idea why? The keyword bid higher on the more specific keyword and it's showing the correct ad for the last search.
Interesting. BTW, If the widget word your targeting gets a lot of traffic, I would get rid of the phrase in the ad group and keep it in just exact. I found reducing the crossover of my ad groups keeps my data 'cleaner' for ad group level optimization.
As for the ads from group widget showing instead of blue widget, the fix above would help that, but also I would wait for traffic to flow in. Part of googles algorithm is CTR, and if your ad copy is more specific in the blue widget group, your going to get a higher CTR and those ads will default anyways 
Hope that answers your question!
PS. I would add in 1 or 2 modified broads to your most specific groups, just to make sure you 'catch' all the odds and ends super specific keywords people search for. Modified broads are *awesome*
I create three adgroup's 1 broad 1 phrase 1 exact of the same adgroup. Add your broad keywords as negative keywords to your exact match adgroup and add your exact match keywords as negatives to your broad match adgroup. Phrase stays as is. Bid higher for exact and phrase match adgroup's...
Thanks for the help guys.
johnaff: I'm using modified broad in a separate group and if it finds a converting keyword, I add it to an exact/phrase group.
I personally recommend doing ad groups from 8-20 words, 80% exact, a few phrase, and a single modified broad, with generous negatives so you weed out low intent words.
I've found this way is the best in terms of getting data evenly spread over each keyword, so its easier to optimize and you are stuck with lots of your keywords getting only like 5 clicks a month, which doesnt help optimization at all.