diff --git a/NAMESPACE b/NAMESPACE
index 2f49382..cf33fa3 100644
--- a/NAMESPACE
+++ b/NAMESPACE
@@ -1,6 +1,9 @@
 # Generated by roxygen2: do not edit by hand
 
 S3method(AIC,fmsm)
+S3method(AICC,flexsurvreg)
+S3method(AICc,flexsurvreg)
+S3method(BIC,flexsurvreg)
 S3method(augment,flexsurvreg)
 S3method(coef,flexsurvreg)
 S3method(glance,flexsurvreg)
@@ -28,6 +31,8 @@ S3method(summary,flexsurvrtrunc)
 S3method(tidy,flexsurvreg)
 S3method(tidy,standsurv)
 S3method(vcov,flexsurvreg)
+export(AICC)
+export(AICc)
 export(Hexp)
 export(Hgamma)
 export(Hgenf)
diff --git a/R/flexsurvreg.R b/R/flexsurvreg.R
index f7c4479..290ee97 100644
--- a/R/flexsurvreg.R
+++ b/R/flexsurvreg.R
@@ -984,12 +984,13 @@ flexsurvreg <- function(formula, anc=NULL, data, weights, bhazard, rtrunc, subse
                   ncovs=ncovs, ncoveffs=ncoveffs,
                   mx=mx, basepars=1:nbpars,
                   covpars=if (ncoveffs>0) (nbpars+1):npars else NULL,
-                  AIC=-2*ret$loglik + 2*ret$npars,
+                  AIC = -2*ret$loglik + 2*ret$npars,
                   data = dat, datameans = colMeans(X),
                   N=nrow(dat$Y), events=sum(dat$Y[,"status"]==1), trisk=sum(dat$Y[,"time"]),
                   concat.formula=f2, all.formulae=forms, dfns=dfns),
              ret,
              list(covdata = covdata)) # temporary position so cyclomort doesn't break
+    ret$BIC <- BIC.flexsurvreg(ret, cens=TRUE)
     if (isTRUE(getOption("flexsurv.test.analytic.derivatives"))
         && (dfns$deriv) ) {
         if (is.logical(fixedpars) && fixedpars==TRUE) { optpars <- inits; fixedpars=FALSE }
@@ -999,6 +1000,7 @@ flexsurvreg <- function(formula, anc=NULL, data, weights, bhazard, rtrunc, subse
     ret
 }
 
+
 ##' @export
 print.flexsurvreg <- function(x, ...)
 {
@@ -1164,10 +1166,17 @@ coef.flexsurvreg <- function(object, ...){
 ##' 
 ##' Number of observations contributing to a fitted flexible survival model
 ##' 
-##' This matches the behaviour of the \code{nobs} method for \code{\link[survival]{survreg}} objects, including both censored and uncensored observations.
+##' By default, this matches the behaviour of the \code{nobs} method for \code{\link[survival]{survreg}} objects, including both censored and uncensored observations.
+##' 
+##' If a weighted \code{flexsurvreg} analysis was done, then this function returns the sum of the weights.
 ##'
 ##' @param object Output from \code{\link{flexsurvreg}} or
 ##' \code{\link{flexsurvspline}}, representing a fitted survival model object.
+##'
+##' @param cens Include censored observations in the number.  \code{TRUE} by default.
+##' If \code{FALSE} then the number of observed events is returned.  See
+##'   \code{\link{BIC.flexsurvreg}} for a discussion of the issues
+##'   with defining the sample size for censored data. 
 ##' 
 ##' @param ... Further arguments passed to or from other methods.  Currently
 ##' unused.
@@ -1183,6 +1192,129 @@ coef.flexsurvreg <- function(object, ...){
 ##' @keywords models
 ##' 
 ##' @export
-nobs.flexsurvreg <- function(object, ...){
-    object$N
+nobs.flexsurvreg <- function(object, cens=TRUE, ...){
+  if (cens) ind <- seq(length.out=nrow(object$data$Y)) else ind <- which(object$data$Y[,"status"] == 1)
+  sum(object$data$m[ind,"(weights)"])
+}
+
+
+##' Bayesian Information Criterion (BIC) for comparison of flexsurvreg models
+##' 
+##' Bayesian Information Criterion (BIC) for comparison of flexsurvreg models
+##' 
+##' @param object Fitted model returned by \code{\link{flexsurvreg}}
+##'   (or \code{\link{flexsurvspline}}).
+##' 
+##' @param cens Include censored observations in the sample size term
+##'   (\code{n}) used in the calculation of BIC.
+##'
+##' @return The BIC of the fitted model.  This is minus twice the log likelihood plus \code{p*log(n)}, where
+##'   \code{p} is the number of parameters and \code{n} is the sample
+##'   size of the data.  If \code{weights} was supplied to
+##'   \code{flexsurv}, the sample size is defined as the sum of the
+##'   weights.
+##'
+##' @param ... Other arguments (currently unused).
+##'
+##' @details There is no "official" definition of what the sample size
+##'   should be for the use of BIC in censored survival analysis.  BIC
+##'   is based on an approximation to Bayesian model comparison using
+##'   Bayes factors and an implicit vague prior.  Informally, the
+##'   sample size describes the number of "units" giving rise to a
+##'   distinct piece of information (Kass and Raftery 1995).  However
+##'   censored observations provide less information than observed
+##'   events, in principle.  The default used here is the number of
+##'   individuals, for consistency with more familiar kinds of
+##'   statistical modelling.  However if censoring is heavy, then the
+##'   number of events may be a better represent the amount of
+##'   information.  Following these principles, the best approximation
+##'   would be expected to be somewere in between.
+##'
+##' AIC and BIC are intended to measure different things.  Briefly,
+##' AIC measures predictive ability, whereas BIC is expected to choose
+##' the true model from a set of models where one of them is the
+##' truth.  Therefore BIC chooses simpler models for all but the
+##' tiniest sample sizes (\eqn{log(n)>2}, \eqn{n>7}).  AIC might be preferred in the
+##' typical situation where
+##' "all models are wrong but some are useful". AIC also gives similar
+##' results to cross-validation (Stone 1977).
+##'
+##' @references Kass, R. E., & Raftery, A. E. (1995). Bayes
+##'   factors. Journal of the American Statistical Association,
+##'   90(430), 773-795.
+##'
+##' @references Stone, M. (1977). An asymptotic equivalence of choice
+##'   of model by cross‐validation and Akaike's criterion. Journal of
+##'   the Royal Statistical Society: Series B (Methodological), 39(1),
+##'   44-47.
+##'
+##' @seealso \code{\link{BIC}}, \code{\link{AIC}}, \code{\link{AICC.flexsurvreg}}, \code{\link{nobs.flexsurvreg}}
+##'
+##' @export
+BIC.flexsurvreg <- function(object, cens = TRUE, ...){
+  n <- nobs.flexsurvreg(object, cens=cens)
+  -2*object$loglik + object$npars * log(n)  
 }
+
+
+##' Second-order Akaike information criterion 
+##'
+##' Second-order or "corrected" Akaike information criterion, often
+##' known as AICc (see, e.g. Burnham and Anderson 2002).  This is
+##' defined as -2 log-likelihood + \code{(2*p*n)/(n - p -1)}, whereas
+##' the standard AIC is defined as -2 log-likelihood + \code{2*p},
+##' where \code{p} is the number of parameters and \code{n} is the
+##' sample size.  The correction is intended to adjust AIC for
+##' small-sample bias, hence it only makes a difference to the result
+##' for small \code{n}.
+##' 
+##' This can be spelt either as \code{AICC} or \code{AICc}.
+##'
+##' @param object Fitted model returned by \code{\link{flexsurvreg}}
+##'   (or \code{\link{flexsurvspline}}).
+##'
+##' @param cens Include censored observations in the sample size term
+##'   (\code{n}) used in this calculation. See
+##'   \code{\link{BIC.flexsurvreg}} for a discussion of the issues
+##'   with defining the sample size.
+##'
+##' @param ... Other arguments (currently unused).
+##'
+##' @references Burnham, K. P., Anderson, D. R. (2002) Model Selection and Multimodel Inference: a practical information-theoretic approach. Second edition. Springer: New York.
+##'
+##' @return The second-order AIC of the fitted model.
+##'
+##' @seealso \code{\link{BIC}}, \code{\link{AIC}}, \code{\link{BIC.flexsurvreg}}, \code{\link{nobs.flexsurvreg}}
+##' 
+##' @export
+AICc.flexsurvreg <- function(object, cens=TRUE, ...){
+  n <- nobs.flexsurvreg(object, cens=cens)
+  p <- object$npars
+## equivalently: object$AIC + ((2 * p) * (p + 1) / (n - p - 1))
+  -2*object$loglik + (2*p*n) / (n - p - 1) 
+}
+
+
+##' @rdname AICc.flexsurvreg
+##' @export
+AICC.flexsurvreg <- AICc.flexsurvreg
+
+##' Second-order Akaike information criterion 
+##' 
+##' Generic function for the second-order Akaike information criterion.
+##' The only current implementation of this in \pkg{flexsurv} is
+##' in \code{\link{AICc.flexsurvreg}}, see there for more details.
+##'
+##' This can be spelt either as \code{AICC} or \code{AICc}.
+##'
+##' @param object Fitted model object.
+##'
+##' @param ... Other arguments (currently unused).
+##'
+##' @export
+AICc <- function (object, ...)
+UseMethod("AICc")
+
+##' @rdname AICc
+##' @export
+AICC <- AICc
diff --git a/man/AICc.Rd b/man/AICc.Rd
new file mode 100644
index 0000000..0889858
--- /dev/null
+++ b/man/AICc.Rd
@@ -0,0 +1,24 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/flexsurvreg.R
+\name{AICc}
+\alias{AICc}
+\alias{AICC}
+\title{Second-order Akaike information criterion}
+\usage{
+AICc(object, ...)
+
+AICC(object, ...)
+}
+\arguments{
+\item{object}{Fitted model object.}
+
+\item{...}{Other arguments (currently unused).}
+}
+\description{
+Generic function for the second-order Akaike information criterion.
+The only current implementation of this in \pkg{flexsurv} is
+in \code{\link{AICc.flexsurvreg}}, see there for more details.
+}
+\details{
+This can be spelt either as \code{AICC} or \code{AICc}.
+}
diff --git a/man/AICc.flexsurvreg.Rd b/man/AICc.flexsurvreg.Rd
new file mode 100644
index 0000000..219d4d5
--- /dev/null
+++ b/man/AICc.flexsurvreg.Rd
@@ -0,0 +1,44 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/flexsurvreg.R
+\name{AICc.flexsurvreg}
+\alias{AICc.flexsurvreg}
+\alias{AICC.flexsurvreg}
+\title{Second-order Akaike information criterion}
+\usage{
+\method{AICc}{flexsurvreg}(object, cens = TRUE, ...)
+
+\method{AICC}{flexsurvreg}(object, cens = TRUE, ...)
+}
+\arguments{
+\item{object}{Fitted model returned by \code{\link{flexsurvreg}}
+(or \code{\link{flexsurvspline}}).}
+
+\item{cens}{Include censored observations in the sample size term
+(\code{n}) used in this calculation. See
+\code{\link{BIC.flexsurvreg}} for a discussion of the issues
+with defining the sample size.}
+
+\item{...}{Other arguments (currently unused).}
+}
+\value{
+The second-order AIC of the fitted model.
+}
+\description{
+Second-order or "corrected" Akaike information criterion, often
+known as AICc (see, e.g. Burnham and Anderson 2002).  This is
+defined as -2 log-likelihood + \code{(2*p*n)/(n - p -1)}, whereas
+the standard AIC is defined as -2 log-likelihood + \code{2*p},
+where \code{p} is the number of parameters and \code{n} is the
+sample size.  The correction is intended to adjust AIC for
+small-sample bias, hence it only makes a difference to the result
+for small \code{n}.
+}
+\details{
+This can be spelt either as \code{AICC} or \code{AICc}.
+}
+\references{
+Burnham, K. P., Anderson, D. R. (2002) Model Selection and Multimodel Inference: a practical information-theoretic approach. Second edition. Springer: New York.
+}
+\seealso{
+\code{\link{BIC}}, \code{\link{AIC}}, \code{\link{BIC.flexsurvreg}}, \code{\link{nobs.flexsurvreg}}
+}
diff --git a/man/BIC.flexsurvreg.Rd b/man/BIC.flexsurvreg.Rd
new file mode 100644
index 0000000..704799a
--- /dev/null
+++ b/man/BIC.flexsurvreg.Rd
@@ -0,0 +1,64 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/flexsurvreg.R
+\name{BIC.flexsurvreg}
+\alias{BIC.flexsurvreg}
+\title{Bayesian Information Criterion (BIC) for comparison of flexsurvreg models}
+\usage{
+\method{BIC}{flexsurvreg}(object, cens = TRUE, ...)
+}
+\arguments{
+\item{object}{Fitted model returned by \code{\link{flexsurvreg}}
+(or \code{\link{flexsurvspline}}).}
+
+\item{cens}{Include censored observations in the sample size term
+(\code{n}) used in the calculation of BIC.}
+
+\item{...}{Other arguments (currently unused).}
+}
+\value{
+The BIC of the fitted model.  This is minus twice the log likelihood plus \code{p*log(n)}, where
+  \code{p} is the number of parameters and \code{n} is the sample
+  size of the data.  If \code{weights} was supplied to
+  \code{flexsurv}, the sample size is defined as the sum of the
+  weights.
+}
+\description{
+Bayesian Information Criterion (BIC) for comparison of flexsurvreg models
+}
+\details{
+There is no "official" definition of what the sample size
+  should be for the use of BIC in censored survival analysis.  BIC
+  is based on an approximation to Bayesian model comparison using
+  Bayes factors and an implicit vague prior.  Informally, the
+  sample size describes the number of "units" giving rise to a
+  distinct piece of information (Kass and Raftery 1995).  However
+  censored observations provide less information than observed
+  events, in principle.  The default used here is the number of
+  individuals, for consistency with more familiar kinds of
+  statistical modelling.  However if censoring is heavy, then the
+  number of events may be a better represent the amount of
+  information.  Following these principles, the best approximation
+  would be expected to be somewere in between.
+
+AIC and BIC are intended to measure different things.  Briefly,
+AIC measures predictive ability, whereas BIC is expected to choose
+the true model from a set of models where one of them is the
+truth.  Therefore BIC chooses simpler models for all but the
+tiniest sample sizes (\eqn{log(n)>2}, \eqn{n>7}).  AIC might be preferred in the
+typical situation where
+"all models are wrong but some are useful". AIC also gives similar
+results to cross-validation (Stone 1977).
+}
+\references{
+Kass, R. E., & Raftery, A. E. (1995). Bayes
+  factors. Journal of the American Statistical Association,
+  90(430), 773-795.
+
+Stone, M. (1977). An asymptotic equivalence of choice
+  of model by cross‐validation and Akaike's criterion. Journal of
+  the Royal Statistical Society: Series B (Methodological), 39(1),
+  44-47.
+}
+\seealso{
+\code{\link{BIC}}, \code{\link{AIC}}, \code{\link{AICC.flexsurvreg}}, \code{\link{nobs.flexsurvreg}}
+}
diff --git a/man/nobs.flexsurvreg.Rd b/man/nobs.flexsurvreg.Rd
index 21f919f..02a912c 100644
--- a/man/nobs.flexsurvreg.Rd
+++ b/man/nobs.flexsurvreg.Rd
@@ -4,12 +4,17 @@
 \alias{nobs.flexsurvreg}
 \title{Number of observations contributing to a fitted flexible survival model}
 \usage{
-\method{nobs}{flexsurvreg}(object, ...)
+\method{nobs}{flexsurvreg}(object, cens = TRUE, ...)
 }
 \arguments{
 \item{object}{Output from \code{\link{flexsurvreg}} or
 \code{\link{flexsurvspline}}, representing a fitted survival model object.}
 
+\item{cens}{Include censored observations in the number.  \code{TRUE} by default.
+If \code{FALSE} then the number of observed events is returned.  See
+  \code{\link{BIC.flexsurvreg}} for a discussion of the issues
+  with defining the sample size for censored data.}
+
 \item{...}{Further arguments passed to or from other methods.  Currently
 unused.}
 }
@@ -22,7 +27,9 @@ model object \code{mod}.  See \code{\link{flexsurvreg}},
 Number of observations contributing to a fitted flexible survival model
 }
 \details{
-This matches the behaviour of the \code{nobs} method for \code{\link[survival]{survreg}} objects, including both censored and uncensored observations.
+By default, this matches the behaviour of the \code{nobs} method for \code{\link[survival]{survreg}} objects, including both censored and uncensored observations.
+
+If a weighted \code{flexsurvreg} analysis was done, then this function returns the sum of the weights.
 }
 \seealso{
 \code{\link{flexsurvreg}}, \code{\link{flexsurvspline}}.
diff --git a/tests/testthat/test_aic.R b/tests/testthat/test_aic.R
new file mode 100644
index 0000000..d11d624
--- /dev/null
+++ b/tests/testthat/test_aic.R
@@ -0,0 +1,17 @@
+test_that("Information criteria",{
+  p <- 3
+  n <- nrow(ovarian)
+  fitg <- flexsurvreg(formula = Surv(ovarian$futime, ovarian$fustat) ~ 1, dist="gengamma")
+  expect_equal(nobs(fitg), n)
+  AIC(fitg)
+  expect_equal(BIC(fitg), AIC(fitg, k=log(n)))
+  nevent <- sum(ovarian$fustat)
+  expect_equal(BIC(fitg, cens=FALSE), AIC(fitg, k=log(nevent)))
+  expect_equal(BIC(fitg), BIC.flexsurvreg(fitg))
+  expect_equal(BIC(fitg,cens=FALSE), BIC.flexsurvreg(fitg,cens=FALSE))
+  expect_equal(AICc(fitg), AIC(fitg, k=(2*n) / (n - p - 1)))
+  expect_equal(AICc(fitg,cens=FALSE), AIC(fitg, k=(2*nevent) / (nevent - p - 1)))
+  expect_equal(AICC(fitg), AICc(fitg))
+  expect_equal(AICc.flexsurvreg(fitg), AICc(fitg))
+  expect_equal(AICC.flexsurvreg(fitg), AICc(fitg))
+})