Choosing equivalent zener diodes from Renesas HZ series

I am trying to find modern equivalents for HZ6A1L and HZ162L zener diodes and I would appreciate it if someone could help me find suitable replacements.

According to the datasheet I found, the HZ6A1L has values of VZmin = 5.2V and VZmax = 5.5V. The closest ones I found for that one are BZX55C5V1 and BZX55C5V6 zeners. Which one would be a better fit?

The HZ162L has values between 15.7V and 16.5V. The closest one I found for that one is BZX55C16.

I'd also appreciate it if someone could explain the ranges in voltage ranges in zener diodes and how they impact the choosing of equivalents.
 

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Can you post the circuit they are used in?
HZ6A1L is a 5.35V, 2.8%, 0.4W Zener diode.

Typical Vz are 5.1V and 5.6V, as you found.
Generally you should keep the same power rating
so the operating point will be similar.
 
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The circuit I am replacing the diodes is from a Japanese class A amplifier, Accuphase P-266.
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Thanks! Could you explain what would happen if I used a 500mW 5.1V zener instead of a 400mW? Why is the power of the zener critical? I always assumed that as long as it is greater than the previous voltage it would be fine.

I recently acquired the amplifier with a broken channel, and I am trying to repair/restore it and learn as much as possible about the design.