I haven't looked closely at this problem but a cursory glance suggests 
that Sqlite is not using an ASC indesx if there is a DESC ORDER By clause.

Try doing the selection ASC and then sorting the output DESC as a 
seperate action.

Alexey Pechnikov wrote:
> Really, there is problem with multi-column indexes. You must use only primary 
> key index for ">=" where clause and "ASC" sorting and "<=" where clause and 
> DESC sorting. 
> 
> 
> 1. I try with primary key:
> 
> #!/usr/bin/tclsh
> package require sqlite3
> sqlite3 db index_order.db
> db eval {DROP TABLE IF EXISTS events}
> db eval {CREATE TABLE events (eid INTEGER PRIMARY KEY,type INTEGER)}
> db transaction {
>     for {set i 0} {$i<100000000} {incr i} {
>         set type [expr {$i % 50}]
>         db eval {insert into events values ($i,$type)}
>     }
> }
> db close
> 
> So, "type" is equal ("eid" mod 50).
> 
> sqlite> SELECT events.* FROM events WHERE eid<=32619760 and type=22 ORDER BY 
> eid DESC LIMIT 1;
> 32619722|22
> CPU Time: user 0.000000 sys 0.000000
> 
> sqlite> EXPLAIN QUERY PLAN SELECT events.* FROM events WHERE eid<=32619760 
> and 
> type=22 ORDER BY eid DESC LIMIT 1;
> 0|0|TABLE events USING PRIMARY KEY ORDER BY
> 
> ========
> Result: this index is good.
> ========
> 
> 2. And I try with two-columns common order index:
> #!/usr/bin/tclsh
> package require sqlite3
> sqlite3 db index_order.db
> db eval {DROP TABLE IF EXISTS events}
> db eval {CREATE TABLE events (eid INTEGER PRIMARY KEY,type INTEGER)}
> db transaction {
>     for {set i 0} {$i<100000000} {incr i} {
>         set type [expr {$i % 50}]
>         db eval {insert into events values ($i,$type)}
>     }
> }
> db eval {CREATE INDEX ev_idx ON events(type,eid)}
> db close
> 
> sqlite> SELECT events.* FROM events WHERE eid<=32619760 and type=22 ORDER BY 
> eid DESC LIMIT 1;
> 32619722|22
> CPU Time: user 1.400088 sys 1.696106
> 
> sqlite> EXPLAIN QUERY PLAN SELECT events.* FROM events WHERE eid<=32619760 
> and 
> type=22 ORDER BY eid DESC LIMIT 1;
> 0|0|TABLE events WITH INDEX ev_idx ORDER BY
> 
> ========
> Result: this index is bad.
> ========
> 
> 3. And I try with two-columns desc order index:
> #!/usr/bin/tclsh
> package require sqlite3
> sqlite3 db index_order.db
> db eval {DROP TABLE IF EXISTS events}
> db eval {CREATE TABLE events (eid INTEGER PRIMARY KEY,type INTEGER)}
> db transaction {
>     for {set i 0} {$i<100000000} {incr i} {
>         set type [expr {$i % 50}]
>         db eval {insert into events values ($i,$type)}
>     }
> }
> db eval {CREATE INDEX ev_desc_idx ON events(type asc,eid desc)}
> db close
> 
> sqlite> SELECT events.* FROM events WHERE eid<=32619760 and type=22 ORDER BY 
> eid DESC LIMIT 1;
> 32619722|22
> CPU Time: user 0.600037 sys 0.608038
> 
> sqlite> EXPLAIN QUERY PLAN SELECT events.* FROM events WHERE eid<=32619760 
> and 
> type=22 ORDER BY eid DESC LIMIT 1;
> 0|0|TABLE events WITH INDEX ev_desc_idx ORDER BY
> 
> 
> And with modified query:
> 
> sqlite> SELECT events.* FROM events WHERE eid>=32619760 and type=22 ORDER BY 
> eid DESC LIMIT 1;
> 99999972|22
> CPU Time: user 0.000000 sys 0.000000
> sqlite> SELECT events.* FROM events WHERE eid<=32619760 and type=22 ORDER BY 
> eid ASC LIMIT 1;
> 22|22
> CPU Time: user 0.000000 sys 0.004000
> sqlite> SELECT events.* FROM events WHERE eid>=32619760 and type=22 ORDER BY 
> eid ASC LIMIT 1;
> 32619772|22
> CPU Time: user 0.284018 sys 0.820051
> 
> 
> 
> ========
> Result: this index is bad.
> ========
> 
> 
> P.S. Try with primary key index only and write your results.
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