For months, I connect to my ISP only about 50% of my attempts.
pppd -d with syslogging of local2.* allowed me to fix a few
things (which brought the connection rate from 25% to its
current 50%).  But I still notice some weirdness w.r.t. IPCP
negotiation during the failed attempts:

pppd[176]: sent [IPCP ConfReq id=0x1 <addr 0.0.0.0> <compress VJ 0f 00>]
pppd[176]: rcvd [IPCP ConfReq id=0x9 <compress VJ 0f 00> <addr 0.0.0.0>]
pppd[176]: sent [IPCP ConfRej id=0x9 <addr 0.0.0.0>]
pppd[176]: sent [IPCP ConfReq id=0x1 <addr 0.0.0.0> <compress VJ 0f 00>]
pppd[176]: rcvd [IPCP ConfReq id=0xa <compress VJ 0f 00> <addr 0.0.0.0>]
pppd[176]: sent [IPCP ConfRej id=0xa <addr 0.0.0.0>]

  This continues for 30 seconds, at which point my machine gives up.

  So, why does my machine ask for <addr> <compress>, and then
reject <compress> <addr>?  Aren't requests 0x1 and 0x9
identical as far as their meaning?  Or is the remote end
supposed to have filled in the 0.0.0.0 in request 0x9 (and 0xa and ...)?

  My options file is appended below.  Thanks for any help -- I
tried looking at the source code, but quickly got lost.

  Brian
-- 
/dev/tty02
115200
defaultroute
crtscts
lock
modem
##  These two end up trying <compress VJ 0f 00>
vj-max-slots 16
novjccomp
mtu 572
mru 572
disconnect '/etc/ppp/ip-down'
connect '/etc/ppp/redialchat'