Keywords:  High-redshift galaxies (734); Galaxy evolution (594); Near infrared astronomy (1093); Poststarburst galaxies (2176); Quenched galaxies (2016);

1. INTRODUCTION

2. OBSERVATIONS
2.1. Photometry and Sample Selection
2.2. Keck / MOSFIRE Observations

3. ANALYSIS
3.1. SED Fitting and Rest-Frame Colors

4. RESULTS
4.1. Quiescent Candidate COS55-128636,  $z_{spec}=3.757$
4.2. The broad-line AGN in COS55-126891,  $z_{spec}=3.594$
4.3. Quiescent Candidate COS55-129098,  $z_{spec}=3.336$
4.4. Quiescent Candidate COS55-126981,  $z_{spec}=4.673$

5. DISCUSSION AND SUMMARY
5.1. Tackling the Age Bias in Quiescent Samples
5.3. Too Big to Be?