There are a number of series that have similar formats and are described as Wee Books for Wee Folks. These familiar little books (5.5 x 4.25) have a small appliqué (3.5 x 2.5) pasted on the cover. This format is seen in:

Series #186 Wee Books for Wee Folks (third format)
Series #187 Wee Folks Bible Stories Series
Series #188 Wee Folks Cinderella Series
Series #189 Wee Folks Peter Rabbit Series
Series #126 Little Sallie Mandy Series
Series #123 Little Black Sambo Series
Series #124 Little Bunnie Bunniekin Series

Examples are noted below:

Today I am adding two more of a very uncommon variant cover for these series. This cover has an appliqué which makes up the entire front cover. Examples are shown below.

Most of these books have book ads for titles that were published in 1928 and 1929. Thus this variant was published in this years. I have yet to see a dust jacket for any of these books but it is most likely exactly the same as the non variant book cover dust jackets.