Let \(f\) be a transcendental meromorphic function in the complex plane, \[ u=f/f^{(k)} \] and \[ \phi=u^n+\sum_{j=0}^{n-2}c_ju^j, \] where \(c_j\) is a small meromorphic function in terms of \(u\). The author finds several conditions on \(f\), \(f^{(k)}\) and \(\phi\) such that \(f\) is of the form \(R\exp(P)\), where \(R\) is a rational function and \(P\) is a polynomial.