Improved fitness will help limit the variation within (e.g., a delayed increase in HR over any rolling hills, etc), but it's next to impossible to limit any spikes altogether, even on a treadmill. Your heart responds to so many forms of stress that even a super deep breath in the midst of a steady effort can affect its rate, regardless of any other stress incurred.
But again, improved fitness (aerobically/metabolically) will help stabilize it to a degree; the HR won't 'jump' at the first sign of stress. More importantly though, you'll see on your graphs less decoupling within a long, steady effort (less HR drift, steadier pace, less slowing). Stick with familiar routes (loops ideally) to compare from week-to-week; this is where some real insight can be had/HADD!