There's lots of research in Human Computer Interaction on this issue and the general concensus is that breadth beats depth (read: wide top level navigation beats nested submenus).
This is the case due to Short Term Memory (STM) storage issues and how STM is affected by both breath and depth. Pointing to some hard research should help your case to your director and designer quite well. Here's a good excerpt from the book Human Computer Interaction:
For very large hierarchies, or complex web navigation structures in general, in fact keeping track of where one is in the hierarchy depth is more likely to be a strain on memory than scanning the list of items being displayed. That is depth is the memory limit.
STM isn't significantly affected when you can see your options, so breadth is generally preferred. Depth forces you to remember what options are where, which can be taxing on memory.
It's also been found that access time is a function of depth. This means a deeper menu structure results in a longer access time. This makes sense considering the points about STM above.
Overall the results are in agreement with those of Kiger
(1984) where it has been proven that access time is
proportional to depth in menu selection.
Here's a nice overview of the of Depth vs Breadth from the UI Design Newsletter(emphasis is mine):
- Too deep is too deep: users have a more difficult time encoding, and consequently navigating, deep sites.
- Too broad is too broad: conversely extremely broad sites (which may encourage satisficing) also present a challenge to efficient
- Effective sub-grouping reduces perceived breadth: grouping navigation elements thematically improves performance for even the
Their conclusion stresses the importance of proper grouping as well. This helps limit short term memory load as logical grouping means I should intuitively know what's under a submenu, I don't have to look to find out.
Bottom line, a lot of research shows deep navigation menus to be slow or confusing. This means each layer of "submenu" as in your question results in slower access times for any items hidden inside the deeper menus. This is a good reason to consider alternatives, such as Mega Menus as others have brought up.