The Halacha permits Shvut D'shvut, instructing a non-Jew to perform a Melacha on Shabbat that is only prohibited M'drabanan (from Rabbinic law), for the sake of a Misva, a sick person or to avoid a major financial loss.
Generally, the prohibitions in the Torah have a minimal measure which must be violated in order to be culpable. For example, one is not culpable for eating forbidden foods until he eats a Kesayit-an olive bulk. There is a discussion as to the status of violating "Hasi Shiur"-less than the minimal measure. While all agree that it is prohibited to do so, the question is whether such a violation is prohibited from the Torah or M'drabanan. If it is prohibited from the Torah, the difference between less and more than the minimum is whether the perpetrator is liable to receive Malkot (lashes).
This Rambam, in his introduction to Hilchot Shabbat, states that performing less than the minimal amount of a Melacha on Shabbat is only liable M'drabanan. For example, the minimum amount of writing deemed a Melacha from the Torah is writing two letters. If one wrote only one letter, he is only liable M'drabanan. Hacham Bension brought a proof to this position from the Tossefta.
This principle is relevant to defining a Shvut D'shvut to instruct a non-Jew to perform a Melacha M'drabanan. For example, if someone is sick with a non-life threatening illness and requires a small quantity of medication to be pulverized, it is permitted to tell a non-Jew to pulverize the medicine less than the minimum measurement. Although pulverising is a Melacha D'oraita, pulverising such a small amount is only prohibited M'drabanan, and therefore, this qualifies as a Shvut D'shvut in a case of sickness.
Another example would be telling a non-Jew to sign a pharmacy receipt in order to provide medicine to someone sick with a non-life threatening illness. If he only signs with a one letter initial, it is less than the minimum measure to constitute a Melacha D'oraita. Therefore, it is permitted to tell him to do so.
Performing less than the prescribed measure of a Melacha on Shabbat is only prohibited M'drabanan. Therefore, it is permitted to instruct a non-Jew to do such an amount for the sake of a Misva, a sick person or to prevent major financial loss.