night-sky lines and the line emission from our targets. Continuum morphologies, where detected, are shown as contours in Figs. \[fig:maps\] to \[fig:maps5\]. Imperfections in the night-sky subtraction and flat fielding, and night-sky line residuals make it unfortunately very difficult to obtain a good sky subtraction from SINFONI cubes, which makes continuum flux measurements very challenging. Typical uncertainties are about 0.3$-$0.5 mag, so that measurements through broad-band filters are more reliable.

Integrated spectral properties of the sample {#ssec:intspec}
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Integrated spectra {#sssec:results.intspec}
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In Fig. \[fig:intspec\] we show the integrated spectra of our targets. Wavelengths between 1.8 $\mu$m and 2.0 $\mu$m, i.e., between the H and K bands, and where the atmospheric transmission is very low, are clipped. For galaxies at redshifts z$\sim 2.0-2.6$, the \[OIII\]$\lambda\lambda$4959,5007 doublet and H$\beta$ fall into the H, and \[OI\]$\lambda$6300, H$\alpha$, \[NII\]$\lambda\lambda$6548,6583, and \[SII\]$\lambda\lambda$6716,6731 fall into the K-band. For galaxies at $z\sim 3.0-3.8$, \[OII\]$\lambda$3727 falls into the H-band and H$\beta$ and \[OIIII\]$\lambda\lambda$4959,5007 fall into the K-band. \[OI\]$\lambda$6300 has been detected in six sources. The \[SII\]$\lambda\lambda$6716,6731 doublet has been detected in 13 sources, and the doublets have been spectrally resolved into individual components in two galaxies. In eleven sources, the two lines of the doublet are blended 