This article contains several uniqueness theorems for meromorphic functions. A typical result is the following one: Let k be a positive integer and \(f_ 1\), \(f_ 2\) be meromorphic with \(\bar N(\)r,f\({}_ j)=S(r,f_ j)\) and \(N(r,f_ j^{-1})-N(r,(f_ j^{(k)})^{- 1})=S(r,f_ j),\) for \(j=1,2\). Let \(a_ 1,...,a_ 4\) and \(b_ 1,...,b_ 4\) be two sets of distinct complex numbers. If any seven of the eight equations \(E(a_{\mu},f_ 1)=E(a_{\mu},f_ 2),\) \(\mu =1,...,4\), and \(E(b_{\nu},f_ 1^{(k)})=E(b_{\nu},f_ 2^{(k)}),\) \(\nu =1,...,4\), hold, where \(E(c,f):=\{z\in {\mathbb{C}}| \quad f(z)=c\},\) then \(f_ 1\equiv f_ 2\).