There are several things you can do, but be aware that putting a good antenna on a handheld introduces other problems, which I'll get to in a moment;
a. It would be most helpful to know where you are (county/state is fine), and to what you are listening. Go to the blue toolbar under the site title on the left, float your mouse over Database, select Frequency Database and use the various pulldowns and maps to get to your area. C'mon back with the URL
b. In your statement you didn't mention anything about how high the antenna is off the ground or whether it's outdoors. In general, outdoors is best and higher is better, but that leads into the next topic, which is;
c. You didn't say anything about the coax you're using. While you can get away with cheap RG58 types if all you're listening to is VHF low band, as you start going higher in frequency, and the antenna gets higher, losses on such runs become correspondingly higher.
Now for the big BUT on this whole shebang - little handhelds like the 405 are not really designed to handle high signal levels very well. There is the possibility of overloading - which can manifest itself as hearing things like pagers and such where you didn't before, or actually losing sensitivity on one or more bands. Additional filtering can and often does improve the situation, but obviously at an increased cost.
A little more information needed here, I think...Mike