I'm sure many of the old hands around here will know these already, but for those who don't yet or may have forgotten, this may come in useful.
https://www.zx81.nl/dload/zx81-memory.pdf
ZX81 1K Space Saving Tips by Sean A Irvine
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ZX81 1K Space Saving Tips by Sean A Irvine
ZX81 with ZiLOG Z84 CMOS Z80, 32KB battery-backed Toshiba 55257 SRAM with charge status LED, Wilf's "Why Wait?" mod and switch-mode 5V regulator. 50/60Hz mode switch, composite video output with Zigg's back porch mod and 1080p60 HDMI output.
Re: ZX81 1K Space Saving Tips by Sean A Irvine
Best saving is coding in machinecode and stop coding in BASIC.
Re: ZX81 1K Space Saving Tips by Sean A Irvine
As an additional comment, if you don't need floating point or flicker free running screen, ZX80 basic is both more efficient on memory and much much faster!