CLUSTER, VACUUM, and TABLESPACEs (oh my)

Hi,

I would like to request a little clarification on the CLUSTER and VACUUM commands. My use case here (partially) is when
mydisk runs out of space and I want to move a table to a newly created tablespace. These questions somewhat overlap.
Let’ssay I am starting with a table that is not CLUSTERed on a given index, but I want it to be. 

* If I run “CLUSTER table USING idx” on a table, is VACUUM FULL required/useful afterwards, or should I assume that the
clusteroperation did the equivalent of a VACUUM FULL? 

* If I have previously run a CLUSTER command on a table, will future VACUUM FULL commands rewrite the table in the
orderspecified in the previous CLUSTER? 

* If I want to move a table to a new tablespace, is it possible to CLUSTER+VACUUM in the same step since the whole
tablewill be rewritten anyway? This would be very useful in low-disk space scenarios. I did find this answer, but it’s
datedseveral years ago and was hoping for something better supported. https://dba.stackexchange.com/a/87457/121020 

The documentation is somewhat silent on these details, so I thought I’d ask here. Right now I move a table to a new
tablespace,cluster on an index, and then do a full vacuum which results in three full copies of the table being
written,which seems less than optimal where one should only be needed as far as I understand things. 

Cheers,
Demitri