Spending more time with the Billboard listing of one-hit wonders, I came across a number of performers who had other singles that IMHO deserved to make the top forty and therefore would have removed those artists from qualifying as one-hit wonders.

I present you with 3 examples:

The Exciters - only top 40 hit (reached #4)  was Tell Him
He's Got The Power (#57) or Get Him (#76) were deserving of making the top 40.

Mark Dinning - only top 40 hit was Teen Angel (reached #1)
The Lovin Touch (#84) or Top 40 News Weather and Sports (#81) were deserving of making the top 40.

The Cleftones - only top 40 hit was Heart and Soul (#18)
For Sentimental Reasons (#60) merited top 40 - one of my all-time favorite doo-wop songs.