Bigger is not always better. As a small hosting provider myself, I have picked up many clients from major providers because I offer a consultative approach to my customers, especially during the pre-sign period where we as a team need to understand their environment, usage patterns and availability requirements. While you may pay a little more, it is completely possible that a smaller provider will take the time to understand what you have and what the issue is before telling you the proper solution. I'm purposely not putting my company info out here as there are many good small providers. Some probably within miles of your office. (Good for going to lunch with them periodically to discuss your concerns/issues/plans.)
As an FYI.. we have had a number of clients using Java apps on previous providers where JAVA was the problem. If you're using java or some java based server, do yourself a favor and get off of it.