According to the [Rao-Blackwell theorem](https://en.wikipedia.org/wiki/Rao%E2%80%93Blackwell_theorem), if statistic $T$ is a sufficient and complete for $\theta$, and $E(T)=\theta$, then $T$ is a uniformly minimum-variance unbiased estimator (UMVUE).

I am wondering how to justify that an unbiased estimator is a UMVUE: 

1. if $T$ is not sufficient, can it be a UMVUE?
2. if $T$ is not complete, can it be a UMVUE?
3. If $T$ is not sufficient or complete, can it be a UMVUE?