During the past 15 years the annual growth rate of tropospheric methane (CH4) has shown striking changes over 2--3 year periods, varying from +1% yr-1 to slightly negative values (-0.2% yr-1). These fluctuations are superimposed on an overall slowdown of the CH4 growth rate since the 1980s. Here we use our complementary measurement of other compounds (ethane, tetrachloroethene) to confirm the influence of biomass burning on large global CH4 pulses in 1998 and 2002--2003. Methane growth rate fluctuations also track ENSO indices, most likely via the influence of ENSO activity on large-scale biomass burning. We also report the seventh year of near-zero growth of global CH4 levels (Dec. 1998--Dec. 2005). The global CH4 mixing ratio was 1772 ¿ 1 ppbv in 2005, and CH4 increases of 118--376 ppbv between 2000--2020 (ten scenarios in the 2001 IPCC report, to levels around 1900+ ppbv by 2020, now appear quite unlikely.