The author of this article draws special attention to two particular claims of the free bankers concerning the supposed working characteristics of a fractional-reserve free banking system which may strike the reader as questionable. The first of these relates to the alleged absence of a real-balance effect under free banking. The second relates to the free bankers´ reference to Walras´ Law as providing a rationale for the free banking system´s “offsetting” actions when confronted with changes in the public´ s demand to hold bank liabilities. This rationale is defective since it is based on an erroneous interpretation of Walras´ Law. The author´s conclusion does not imply that it is not at all possible, from a rational viewpoint, to make a plausible case for this variant of free banking, only that the argument should be freed from certain questionable tenets