Problem posting links


I have some problems posting links, when i use the tweet doesn’t show up in search, if i use my own site url(shows when hovering), the tweet doesn’t show up in search.
If i leave out the link, the tweet shows up in search.
This goes for Top, All and People you follow.

It seems dat and are not safe to use according to

So what url shortening service must i use to get my tweets viewable in search with a link in it?