Quick note: the minimum brightness of the Xperia z1 compact is quite high. With root it can easily be set lower even on the stock ROM:
allows arbitrary brightness settings (replace 25 by a number between 1 and 255). Entering it on the console is a bit cumbersome so I made a tasker profile for it. You can download it as an app. In the app, brightness is fixed at 25, my optimum value for using the screen in the darkness. here, Source code for the task (in case you want to use it in your own tasker) here:
Backlight Low (3) A1: Run Shell [ Command:echo >/sys/class/leds/wled\:backlight/brightness Timeout (Seconds):0 Use Root:On Store Output In: Store Errors In: Store Result In: ]
brightness only stays low until set from another source overwrites it, so if you set it to zero (I know somebody will) switching the device off and on again should fix it. Using in changing light conditions needs more thought to prevent auto brightness from overwriting the value.
Disclaimer: if you accidentally harm your device using materials from here it is your own responsibility.