How can I match a time entry to a project?

I have created a Project under a Customer and added a time entry. I clicked on "Save and Add New" to add a second time entry but the only option then is to add it under the Customer, not under the Project. The project doesn't appear in the drop-down list of options. 

So now only one entry is under the Project but both show up under the Customer's transactions. I want them all to appear under the Project, as I have multiple Projects for this Customer. 

Any suggestions? Thanks!