A frame is called scalable, if there exists nonnegative scalars such that column weighted frame is tight. A scaling is called a minimal scaling if it does not contain a proper subscaling. We call a minimal scaling as a sparsest minimal if the cardinality of the support of the scaling is minimal. The objective of the present work is to find a sparsest minimal scaling. We also discuss the uniqueness of sparsest minimal scaled frames as a good candidate for incoherent tight frames in recovering sparse signals. © 2018 IEEE.