Not only could you send babies by parcel post, one guy mailed a bank in 1916.
The freight charges to ship the bricks to Vernal were about 4 times more expensive than what the bricks cost. In a stroke of creative genius, Coltharp decided he would have the bricks mailed to the small town, taking advantage of the cheap parcel post rates.
As the post offices began to get overwhelmed by the cartons of bricks, the postmasters began to get frantic. Ultimately the entire quota of bricks were delivered, but the post office changed their regulations. The new rules stipulated that the sender and receiver could only ship or receive a total of 200 pounds of goods in a single day. In a clarification of the rule, the postal administration indicated that "it is not the intent of the United States Postal Service that buildings be shipped through the mail." [Link, via Neatorama]