A few interesting designs at this web site
[http://members.tripod.com/~KE4UYP/index-22.html] may help you.

One is a a linear loaded 1/2 wave inverted L fed at the top of the L
rather than the base.

Another is a top & bottomed hatted, bottom fed L.

Neither design requires radials.

Author includes theoretical radiation patterns & SWR curves.

73

Terry
W9EJO