Let f ( z ) = z + a 2 z 2 + ⋯ f(z) = z + {a_2}{z^2} + \cdots be analytic in the unit disc U U and let k ( z ) = z / ( 1 − z ) k(z) = z/(1 - z) . The classic Marx-Strohhäcker result, that a convex (univalent) function f f is starlike of order 1 2 \frac {1}{2} , can be written in terms of differential subordinations as \[ z f ( z ) / f ′ ( z ) ≺ z k ( z ) / k ′ ( z ) ⇒ z f ′ ( z ) / f ( z ) ≺ z k ′ ( z ) / k ( z ) . zf(z)/f’(z) \prec zk(z)/k’(z) \Rightarrow zf’(z)/f(z) \prec zk’(z)/k(z). \] The authors determine general conditions on k k for which this relation holds. They also determine a different set of general conditions on k k for which \[ z f ′ ( z ) / f ( z ) ≺ z k ′ ( z ) / k ( z ) ⇒ f ( z ) / z ≺ k ( z ) / z . zf’(z)/f(z) \prec zk’(z)/k(z) \Rightarrow f(z)/z \prec k(z)/z. \] Finally, differential subordinations with starlike superordinate functions are considered.