Gigabyte is creating an RTX 4060 low-profile card: https://www.tomshardware.com/news/gigabyte-geforce-rtx-4060-set-to-be-the-first-low-profile-ada-lovelace-design
3 fans, single 8-pin, 2 slots.
Pie in the sky, but would love to see an RTX 4060ti (or more crazy RTX 4070) model at some point.
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16/01/2023 Addendum
ASUS now has a 4060 Low Profile card.
188mm, triple fan.
[URL unfurl="true"]https://www.asus.com/motherboards-components/graphics-cards/asus/rtx4060-8g-lp-brk/[/URL]
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19/04/2024 Addendum
Galax has a card
182mm, triple fan, but the PCIE cable is at the front which will affect clearance without a custom solution.
Will advise to look for something slightly bigger
[URL unfurl="true"]https://www.kuroutoshikou.com/product/release/gk-rtx4060-e8gb-white-lp.html#product-specification[/URL]
Cases these will fit into (double check before you buy, not everything is available):
Lenovo P3/P360 ULTRA - 182mm* - Gigabyte (May require modding)/Adapter Needed
ZS A4DC V3 - 182mm* - Gigabyte (May require modding)
ZS D2 (D Config) - 182mm - Gigabyte/GALAX (Possible PCIE cable issue)
Gemcase C9 - 182mm - Gigabyte/GALAX (Possible PCIE cable issue)
Lone Industries L5 - 185mm - Gigabyte/GALAX (Consider PCIE adapter)
Custom_Mod SL3 STL 4.8L Rev.1 - 185mm - Gigabyte/GALAX (Consider PCIE adapter)
n3rdware Yocto - 185mm** (Guidance rather than a limit) - Gigabyte/GALAX (Consider PCIE adapter)
n3rdware Yocto+ - 185mm** Guidance rather than a limit) - Gigabyte/GALAX (Consider PCIE adapter)
ZS D2 V2 - 186mm - Gigabyte/GALAX (Consider PCIE adapter)
Custom_Mod Case MINI LP edit. - 190mm - Gigabyte/ASUS/GALAX (Consider PCIE adapter)
J-Hack Pure MK2 - 190mm - Gigabyte/ASUS/GALAX (Consider PCIE adapter)
Lazer3D HT5 - 194mm - Gigabyte/ASUS/GALAX
Lazer3D Cravo - 195mm - Gigabyte/ASUS/GALAX
CAPTAIN CASE V9 - 208mm - Gigabyte/ASUS/GALAX
REVOCCASES N0RDR1 Nano EVO - 210mm - Gigabyte/ASUS/GALAX
Metalfish 2 Plus - 210mm - Gigabyte/ASUS/GALAX
LZmod A24-V5 V2.0 - 220mm- Gigabyte/ASUS/GALAX
Silverstone Milo ML03 - 223mm - Gigabyte/ASUS/GALAX
Silverstone Milo ML04 - 223mm - Gigabyte/ASUS/GALAX
Metalfish G5 - 245mm*** - Gigabyte/ASUS/GALAX (MATX Board width)
Bug C1 - 245mm*** - Gigabyte/ASUS/GALAX (MATX Board width)
SKTC A10 - 245mm*** - Gigabyte/ASUS/GALAX (MATX Board width)
Silverstone Milo ML11 - 272mm - Gigabyte/ASUS/GALAX