Jelly Bean search - only contacts and apps? In previous versions of Android, the Google search widget allow you to choose what you want to search.
I always configured it to search only contacts and apps. this way the Google web search results doesn't push down the phone search results, and still I can use the widget to search Google.

It seems like in Jelly Bean you can't remove the web search results and they always push the phone search results down (an sometimes even hide them under "Phone Search").

Is there a way to remove the web search results from the widget search?

If not, do you know any efficient search widget/app the can search the phone?
The Universal Search function had to be limited on newer Android versions due to one of Apple's lawsuits. Thanks to this, the search behaviour had to be modified and can't be restored without rooting the device.

For rooted devices the situation is somewhat better since you can replace GoogleQuickSearch.apk with a modified version. You can see the steps on XDA. As always with modifications requiring root, use caution. I'm not certain if the APK is device-dependant.