diff --git a/R/absoluteRanges.R b/R/absoluteRanges.R
index 73f903a..d04302d 100644
--- a/R/absoluteRanges.R
+++ b/R/absoluteRanges.R
@@ -11,20 +11,20 @@
 normarg_seqlengths <- function(seqlengths)
 {
     if (!is.numeric(seqlengths)) 
-        stop("'seqlengths' must be a non-empty numeric vector")
+        stop(wmsg("'seqlengths' must be a non-empty numeric vector"))
     if (length(seqlengths) == 0L)
         return(setNames(integer(0), character(0)))
     seqlengths_names <- names(seqlengths)
     if (is.null(seqlengths_names)) 
-        stop("'seqlengths' must be named")
+        stop(wmsg("'seqlengths' must be named"))
     if (any(seqlengths_names %in% c(NA_character_, ""))) 
-        stop("'seqlengths' has names that are NA or the empty string")
+        stop(wmsg("'seqlengths' has names that are NA or the empty string"))
     if (any(duplicated(seqlengths_names))) 
-        stop("'seqlengths' has duplicated names")
+        stop(wmsg("'seqlengths' has duplicated names"))
     if (!is.integer(seqlengths)) 
         seqlengths <- setNames(as.integer(seqlengths), seqlengths_names)
     if (any(seqlengths < 0L, na.rm=TRUE))
-        stop("'seqlengths' contains negative values")
+        stop(wmsg("'seqlengths' contains negative values"))
     seqlengths
 }
 
@@ -61,7 +61,7 @@ isSmallGenome <- function(seqlengths)
 absoluteRanges <- function(x)
 {
     if (!is(x, "GenomicRanges"))
-        stop("'x' must be a GenomicRanges object")
+        stop(wmsg("'x' must be a GenomicRanges object"))
     x_seqlengths <- seqlengths(x)
     if (!isTRUE(isSmallGenome(x_seqlengths)))
         stop(wmsg("the total length of the underlying sequences is too big ",
@@ -87,7 +87,7 @@ absoluteRanges <- function(x)
 relativeRanges <- function(x, seqlengths)
 {
     if (!is(x, "Ranges"))
-        stop("'x' must be a Ranges object")
+        stop(wmsg("'x' must be a Ranges object"))
     if (is.numeric(seqlengths)) {
         ans_seqlengths <- normarg_seqlengths(seqlengths)
         ans_seqinfo <- Seqinfo(seqnames=names(ans_seqlengths),
@@ -104,15 +104,23 @@ relativeRanges <- function(x, seqlengths)
         stop(wmsg("the total length of the sequences specified ",
                   "thru 'seqlengths' is too big or couldn't be ",
                   "computed (because some lengths are NA)"))
-    offsets <- c(0L, cumsum(unname(ans_seqlengths)[-length(ans_seqlengths)]))
-    chrom_starts <- offsets + 1L
-    start2chrom <- findInterval(start(x), chrom_starts)
-    end2chrom <- findInterval(end(x), chrom_starts)
-    if (!identical(start2chrom, end2chrom))
-        stop(wmsg("Some ranges in 'x' are crossing sequence boundaries. ",
+    offsets <- c(0L, cumsum(unname(ans_seqlengths)))
+
+    ## Map each range in 'x' to a sequence in the genome.
+    ticks <- offsets + 1L
+    start2seqid <- findInterval(start(x), ticks)
+    end2seqid <- findInterval(end(x),  ticks)
+    if (!identical(start2seqid, end2seqid))
+        stop(wmsg("Some ranges in 'x' cannot be mapped to a sequence in the ",
+                  "genome because they cross sequence boundaries. ",
                   "Cannot convert them into relative ranges."))
-    ans_ranges <- shift(x, shift=-offsets[start2chrom])
-    ans_seqnames <- names(ans_seqlengths)[start2chrom]
+    if (any(start2seqid < 1L) || any(start2seqid > length(ans_seqlengths)))
+        stop(wmsg("Some ranges in 'x' cannot be mapped to a sequence in the ",
+                  "genome because they are outside the boundaries of the ",
+                  "genome. Cannot convert them into relative ranges."))
+
+    ans_ranges <- shift(x, shift=-offsets[start2seqid])
+    ans_seqnames <- names(ans_seqlengths)[start2seqid]
     GRanges(ans_seqnames, ans_ranges, seqinfo=ans_seqinfo)
 }
 
diff --git a/man/absoluteRanges.Rd b/man/absoluteRanges.Rd
index 375e8d3..6a4621d 100644
--- a/man/absoluteRanges.Rd
+++ b/man/absoluteRanges.Rd
@@ -46,13 +46,19 @@ isSmallGenome(seqlengths)
 }
 
 \details{
-  Because ranges in Bioconductor are using integer vectors for their
-  internal representation, \code{absoluteRanges} and \code{relativeRanges}
-  cannot be used on genomes for which the total sequence length is >
-  \code{.Machine$integer.max}. Utility function \code{isSmallGenome} is
-  provided as a mean for the user to check upfront whether the size of a
-  genome is <= \code{.Machine$integer.max}, and thus compatible with
-  \code{absoluteRanges} and \code{relativeRanges}.
+  Because \code{absoluteRanges} returns the \emph{absolute} ranges in an
+  \link[IRanges]{IRanges} object, and because an \link[IRanges]{IRanges}
+  object cannot hold ranges with an end > \code{.Machine$integer.max}
+  (i.e. >= 2^31 on most platforms), \code{absoluteRanges} cannot be used
+  if the size of the underlying genome (i.e. the total length of the
+  sequences in it) is > \code{.Machine$integer.max}. Utility function
+  \code{isSmallGenome} is provided as a mean for the user to check
+  upfront whether the genome is \emph{small} (i.e. its size is <=
+  \code{.Machine$integer.max}) or not, and thus compatible with
+  \code{absoluteRanges} or not.
+
+  \code{relativeRanges} applies the same restriction by looking at the
+  \code{seqlengths} argument.
 }
 
 \value{
@@ -106,27 +112,50 @@ stopifnot(all(gr == gr2))
 ## ON REAL DATA
 ## ---------------------------------------------------------------------
 
+## With a "small" genome
+
 library(TxDb.Dmelanogaster.UCSC.dm3.ensGene)
 txdb <- TxDb.Dmelanogaster.UCSC.dm3.ensGene
-isSmallGenome(txdb)
 ex <- exons(txdb)
 ex
 
-ar <- absoluteRanges(ex)
-ar
+isSmallGenome(ex)
 
-ex2 <- relativeRanges(ar, seqlengths(ex))
-ex2  # original strand is not restored
-strand(ex2) <- strand(ex)  # set it back
-stopifnot(all(ex == ex2))
+## Note that because isSmallGenome() can return NA (see Value section
+## above), its result should always be wrapped inside isTRUE() when
+## used in an if statement:
+if (isTRUE(isSmallGenome(ex))) {
+    ar <- absoluteRanges(ex)
+    ar
+
+    ex2 <- relativeRanges(ar, seqlengths(ex))
+    ex2  # original strand is not restored
+
+    ## Sanity check:
+    strand(ex2) <- strand(ex)  # restore the strand
+    stopifnot(all(ex == ex2))
+}
+
+## With a "big" genome (but we can reduce it)
 
 library(TxDb.Hsapiens.UCSC.hg19.knownGene)
 txdb <- TxDb.Hsapiens.UCSC.hg19.knownGene
-isSmallGenome(txdb)
-if (interactive()) {
-    ex <- exons(txdb)
+ex <- exons(txdb)
+isSmallGenome(ex)
+\dontrun{
     absoluteRanges(ex)  # error!
 }
+
+## However, if we are only interested in some chromosomes, we might
+## still be able to use absoluteRanges():
+seqlevels(ex, force=TRUE) <- paste0("chr", 1:10)
+isSmallGenome(ex)  # TRUE!
+ar <- absoluteRanges(ex)
+ex2 <- relativeRanges(ar, seqlengths(ex))
+
+## Sanity check:
+strand(ex2) <- strand(ex) 
+stopifnot(all(ex == ex2))
 }
 
 \keyword{manip}