I think the first thing some might tell you is to change to a different antenna! 
Even though I no longer prefer the OCFD for the majority of my applications, there are some things you can do to it to improve reception, and I can still recommend it if you can live with the limitations of its unpredictable nature.
Rather than go into a frenzy of EZnec plots, I'll summarize some of the aspects of what this antenna really is. (canonical version is a 4-foot wire and a 1.5-foot wire attached to the side of a 4:1 tv-type balun (300-75 ohm "balun" and the feedline coming away from it perpendicularly for a few feet or more horizontally)
1) This is not really an off-center fed dipole anymore, because the feedline braid is actually part of the antenna unless you use rf-choking techniques to remove it electrically.
2) Unchoked, the feedline seems more like a very large single-wire groundplane.
3) If you model only the two vertical elements, yes it does seem that the directional lobes get progressively higher and higher. Once you go past about 300mhz, the angles can start to get a bit ridiculously high. 800 mhz is nearly straight up. (This *may* not be an issue if the systems you listen to are strong enough that this isn't a problem, but for many this is the first thing one notices)
4) However, with the addition of the feedline acting as a single-wire horizontal groundplane, things get very weird. Depending on frequency, some lobes may actually come back down a bit, others "fill in", AND you are no longer truly omnidirectional. So in some cases, it may not be actually as bad as you think.
Getting to the point - because every OCFD installation is going to be different and unpredictable, mainly due to the length and direction the feedline is shaped in, it is one of those antennas that you just have to put up and try. What works for you might not for your neighbor.
If you want to experiment, here are a few things you can try to improve reception:
1) Move the horizontal feedline around the compass points and do a test listening-session since the "one wire" feedline groundplane affects not only the vertical lobes, but also the azimuth to a degree.
2) Bend the lower-hanging 1.5 foot element away from vertical, to perhaps 45 degrees or more towards horizontal. You can kind of see that the antenna is now really starting to take on a more typical groundplane shape. If you do this, I'd also start out by making sure that this newly bent element is in the same plane as the feedline.
3) Choke the feedline at the feedpoint with either ferrites, coax-coils, or pawsey stubs. Instead of choking at the feedpoint, you could also try controlling the common-mode of the braid by choking it at the 1/4 wave point if you have a favored band.
4) Add more 1.5 foot "radials" to the system, or perhaps 1/4 radials cut for some other band.
Diminishing returns: at some point, nothing you do may make this antenna perform very well and will end up in the trash in 5 minutes - yet your friend is extremely happy and has one made out of 4-inch copper pipe up at 60 feet.
I guess that is what makes this antenna fun to tinker with, or something that is a total waste of time. It is up to you since there are too many variables to deal with - each installation is unique and unpredictable.
The thing that has been hammered home to me is that unless you get the feedline under control, the antenna is a frankenstein combination of groundplane and dipole. "Frankenpole" anyone?
Even though I no longer prefer the OCFD for the majority of my applications, there are some things you can do to it to improve reception, and I can still recommend it if you can live with the limitations of its unpredictable nature.
Rather than go into a frenzy of EZnec plots, I'll summarize some of the aspects of what this antenna really is. (canonical version is a 4-foot wire and a 1.5-foot wire attached to the side of a 4:1 tv-type balun (300-75 ohm "balun" and the feedline coming away from it perpendicularly for a few feet or more horizontally)
1) This is not really an off-center fed dipole anymore, because the feedline braid is actually part of the antenna unless you use rf-choking techniques to remove it electrically.
2) Unchoked, the feedline seems more like a very large single-wire groundplane.
3) If you model only the two vertical elements, yes it does seem that the directional lobes get progressively higher and higher. Once you go past about 300mhz, the angles can start to get a bit ridiculously high. 800 mhz is nearly straight up. (This *may* not be an issue if the systems you listen to are strong enough that this isn't a problem, but for many this is the first thing one notices)
4) However, with the addition of the feedline acting as a single-wire horizontal groundplane, things get very weird. Depending on frequency, some lobes may actually come back down a bit, others "fill in", AND you are no longer truly omnidirectional. So in some cases, it may not be actually as bad as you think.
Getting to the point - because every OCFD installation is going to be different and unpredictable, mainly due to the length and direction the feedline is shaped in, it is one of those antennas that you just have to put up and try. What works for you might not for your neighbor.
If you want to experiment, here are a few things you can try to improve reception:
1) Move the horizontal feedline around the compass points and do a test listening-session since the "one wire" feedline groundplane affects not only the vertical lobes, but also the azimuth to a degree.
2) Bend the lower-hanging 1.5 foot element away from vertical, to perhaps 45 degrees or more towards horizontal. You can kind of see that the antenna is now really starting to take on a more typical groundplane shape. If you do this, I'd also start out by making sure that this newly bent element is in the same plane as the feedline.
3) Choke the feedline at the feedpoint with either ferrites, coax-coils, or pawsey stubs. Instead of choking at the feedpoint, you could also try controlling the common-mode of the braid by choking it at the 1/4 wave point if you have a favored band.
4) Add more 1.5 foot "radials" to the system, or perhaps 1/4 radials cut for some other band.
Diminishing returns: at some point, nothing you do may make this antenna perform very well and will end up in the trash in 5 minutes - yet your friend is extremely happy and has one made out of 4-inch copper pipe up at 60 feet.
I guess that is what makes this antenna fun to tinker with, or something that is a total waste of time. It is up to you since there are too many variables to deal with - each installation is unique and unpredictable.
The thing that has been hammered home to me is that unless you get the feedline under control, the antenna is a frankenstein combination of groundplane and dipole. "Frankenpole" anyone?
