Connally’s first painting career was spent as an illustrator. Known as a fine artist of advertising, Connally’s paintings won several national awards and were published in numerous national magazines. Her works were regularly included in these shows, New York Society of Illustrators 1980-1995, LA Society of Illustrators 1982, Dallas Society of Illustrators 1980-1995 (Best of Show 3 times), Dallas Society of Visual Communications 1980-1995 (several gold and silver medals), Communication Arts Illustration Annual 1987, The Chicago Show 1980, Graphis Art Annual 1988, Wichita Art Directors 1975-80 (Best of Show twice), Graphix 10 1979 (Best of Ten), Kansas City Art Directors 1981(Bronze metal), D’Art Portrait Show, “100 of Tomorrow’s Greats,” and The Master Eagle Gallery, NY, NY 1980.