  A detailed investigation of lowest excitations in two-dimensional Gaussian
spin glasses is presented. We show the existence of a new zero-temperature
exponent lambda describing the relative number of finite-volume excitations
with respect to large-scale ones. This exponent yields the standard thermal
exponent of droplet theory theta through the relation, theta=d(lambda-1). Our
work provides a new way to measure the thermal exponent theta without any
assumption about the procedure to generate typical low-lying excitations. We
find clear evidence that theta < theta_{DW} where theta_{DW} is the thermal
exponent obtained in domain-wall theory showing that MacMillan excitations are
not typical.
