I would suggest you to reduce the template DNA and according to the primer annealing temperature you can increase the annealing temperature in the PCR machine. And also you can use additives such as 2% or 7% DMSO , 1Molar or 1.5Molar Betaine solution. Yield and specificity increases when you use these additives.
Smears indicate that non-specific amplification is happening in the PCR. It can be due to many reasons, like more template, excessive extension time, low annealing temperature, etc. Since you say that you have smears near the wells, the most probable reason may be more templates copies. Try to reduce the template copies. If this doesn't work out, try increasing the annealing temp, reducing the annealing & extension times. Sometimes the number of cycles also causes smear. Try reducing the number of cycles if still you don't get. Let us know if it worked or not.
I vote for annealing temp. Increase this parametrs and look what you have got. Do not introduce a lot of changes into your initial protocol at the same time. Go step by step.
I agree that it's probably non-specific amplification and you should increase annealing temperature first. You may also want to run some of your (non-PCR'ed) template on a gel.. if you see smearing from that, it's indicating that your template is probably degraded.