diff --git a/NEWS.md b/NEWS.md
index 5ed164b..b23c289 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -1,5 +1,9 @@
 # parsedate (development version)
 
+* Some issues with different formats (e.g. "2000" and "2000-11") could have
+  given inaccurate results previously.  Those are now resolved (#36)
+* Breaking change: fractional seconds are now included (#44)
+
 # parsedate 1.3.1
 
 No user visible changes.
diff --git a/R/parsedate-package.r b/R/parsedate-package.r
index fa48404..f8c692c 100644
--- a/R/parsedate-package.r
+++ b/R/parsedate-package.r
@@ -191,10 +191,13 @@ parse_iso_8601 <- function(dates, default_tz = "UTC") {
 
 parse_iso_parts <- function(mm, default_tz) {
 
+  # Ensure that all fractions use periods rather than commas and are numeric
+  mm$frac <- as.numeric(sub(",", ".", mm$frac))
+  mm$sec <- as.numeric(sub(",", ".", mm$sec))
+
   num <- nrow(mm)
 
-  ## -----------------------------------------------------------------
-  ## Date first
+  ## Date first ----
 
   date <- .POSIXct(rep(NA_real_, num), tz = "")
 
@@ -220,10 +223,9 @@ parse_iso_parts <- function(mm, default_tz) {
 
   ## Years
   fy <- is.na(date)
-  date[fy] <- ymd(paste(mm$year, "01", "01"))
+  date[fy] <- ymd(paste(mm$year[fy], "01", "01"))
 
-  ## -----------------------------------------------------------------
-  ## Now the time
+  ## Now the time ----
 
   th <- mm$hour != ""
   date[th] <- date[th] + hours(mm$hour[th])
@@ -231,36 +233,35 @@ parse_iso_parts <- function(mm, default_tz) {
   tm <- mm$min != ""
   date[tm] <- date[tm] + minutes(mm$min[tm])
 
-  ts <- mm$sec != ""
+  ts <- !is.na(mm$sec)
   date[ts] <- date[ts] + seconds(mm$sec[ts])
 
-  ## -----------------------------------------------------------------
-  ## Fractional time
-
-  frac <- as.numeric(sub(",", ".", mm$frac))
+  ## Fractional time ----
 
-  tfs <- !is.na(frac) & mm$sec != ""
-  date[tfs] <- date[tfs] + milliseconds(round(frac[tfs] * 1000))
+  tfs <- !is.na(mm$frac) & !is.na(mm$sec)
+  # only supporting up to millisecond resolution, rounding subsequent digits
+  date[tfs] <- date[tfs] + milliseconds(round(mm$frac[tfs] * 1000))
 
-  tfm <- !is.na(frac) & mm$sec == "" & mm$min != ""
-  sec <- trunc(frac[tfm] * 60)
-  mil <- round((frac[tfm] * 60 - sec) * 1000)
+  tfm <- !is.na(mm$frac) & is.na(mm$sec) & mm$min != ""
+  sec <- trunc(mm$frac[tfm] * 60)
+  # only supporting up to millisecond resolution, rounding subsequent digits
+  mil <- round((mm$frac[tfm] * 60 - sec) * 1000)
   date[tfm] <- date[tfm] + seconds(sec) + milliseconds(mil)
 
-  tfh <- !is.na(frac) & mm$sec == "" & mm$min == ""
-  min <- trunc(frac[tfh] * 60)
-  sec <- trunc((frac[tfh] * 60 - min) * 60)
-  mil <- round((((frac[tfh] * 60) - min) * 60 - sec) * 1000)
+  tfh <- !is.na(mm$frac) & is.na(mm$sec) & mm$min == ""
+  min <- trunc(mm$frac[tfh] * 60)
+  sec <- trunc((mm$frac[tfh] * 60 - min) * 60)
+  mil <- round((((mm$frac[tfh] * 60) - min) * 60 - sec) * 1000)
   date[tfh] <- date[tfh] + minutes(min) + seconds(sec) + milliseconds(mil)
 
-  ## -----------------------------------------------------------------
-  ## Time zone
+  ## Time zone ----
 
   ftzpm <- mm$tzpm != ""
   m <- ifelse(mm$tzpm[ftzpm] == "+", -1, 1)
   ftzpmh <- ftzpm & mm$tzhour != ""
   date[ftzpmh] <- date[ftzpmh] + m * hours(mm$tzhour[ftzpmh])
   ftzpmm <- ftzpm & mm$tzmin != ""
+  m <- ifelse(mm$tzpm[ftzpmm] == "+", -1, 1)
   date[ftzpmm] <- date[ftzpmm] + m * minutes(mm$tzmin[ftzpmm])
 
   ftzz <- mm$tz == "Z"
@@ -282,18 +283,31 @@ parse_iso_parts <- function(mm, default_tz) {
 }
 
 iso_regex <- paste0(
+  # whitespace at the beginning
   "^\\s*",
+  # the year
   "(?<year>[\\+-]?\\d{4}(?!\\d{2}\\b))",
+  # The dash between year and month
   "(?:(?<dash>-?)",
+   # The month
    "(?:(?<month>0[1-9]|1[0-2])",
+    # The dash between month and day, and the day
     "(?:\\g{dash}(?<day>[12]\\d|0[1-9]|3[01]))?",
+    # or the week
     "|W(?<week>[0-4]\\d|5[0-3])(?:-?(?<weekday>[1-7]))?",
+    # or the yearday
     "|(?<yearday>00[1-9]|0[1-9]\\d|[12]\\d{2}|3",
       "(?:[0-5]\\d|6[1-6])))",
+   # the "T" then the hour
    "(?<time>[T\\s](?:(?:(?<hour>[01]\\d|2[0-3])",
+            # the colon then the minute, and allow for the hour:minute to be
+            # specified as "24:00"
             "(?:(?<colon>:?)(?<min>[0-5]\\d))?|24\\:?00)",
+           # the fraction after the minute
            "(?<frac>[\\.,]\\d+(?!:))?)?",
-    "(?:\\g{colon}(?<sec>[0-5]\\d)(?:[\\.,]\\d+)?)?",
+    # the colon after the minute and the second with its optional fraction
+    "(?:\\g{colon}(?<sec>[0-5]\\d(?:[\\.,]\\d+)?))?",
+    # the timezone as "Z" or "+-hh" or "+-hh:mm" or "+-hhmm"
     "(?<tz>[zZ]|(?<tzpm>[\\+-])",
      "(?<tzhour>[01]\\d|2[0-3]):?(?<tzmin>[0-5]\\d)?)?)?)?$"
   )
diff --git a/tests/testthat/test-corner-cases.R b/tests/testthat/test-corner-cases.R
index f0e3fa4..394bbde 100644
--- a/tests/testthat/test-corner-cases.R
+++ b/tests/testthat/test-corner-cases.R
@@ -73,3 +73,64 @@ test_that("zero length input (issue #20)", {
     parse_iso_8601(character(0)),
     structure(numeric(0), class = c("POSIXct", "POSIXt"), tzone = "UTC"))
 })
+
+test_that("multiple date formats do not cause a warning (issue #36)", {
+  expect_silent(
+    parse_iso_8601(c("2020-03", "2020"))
+  )
+  expect_equal(
+    parse_iso_8601(c("2020-03", "2020")),
+    as.POSIXct(c("2020-03-01", "2020-01-01"), tz = "UTC")
+  )
+
+  # a related set of tests that causes a similar issue to #36, but was not
+  # reported in that issue.  This covers when minute and non-minute timezones
+  # are provided at the same time.
+  valid_datetimes <-
+    c(
+      "2024-08-03T01:02:03Z", # Zulu timezone
+      "2024-08-03T01:02:03+00", # Zulu timezone as numeric
+      "2024-08-03T01:02:03-04", # negative hour timezone without minutes
+      "2024-08-03T01:02:03+04", # positive hour timezone without minutes
+      "2024-08-03T01:02:03-04:00", # negative hour timezone with minutes
+      "2024-08-03T01:02:03+04:15", # positive hour timezone with minutes
+      "2024-08-03T01:02:03.123+04:15" # positive hour timezone with minutes and fractional seconds
+    )
+  expect_silent(
+    parse_iso_8601(valid_datetimes)
+  )
+  expect_equal(
+    parse_iso_8601(valid_datetimes),
+    as.POSIXct(c("2024-08-03 01:02:03", "2024-08-03 01:02:03", "2024-08-03 05:02:03", "2024-08-02 21:02:03", "2024-08-03 05:02:03", "2024-08-02 20:47:03", "2024-08-02 20:47:03.123"), tz = "UTC")
+  )
+})
+
+test_that("capture fractional seconds (issue #44)", {
+  expect_equal(
+    parse_iso_8601("2024-08-03T01:02:03.123+04:15"),
+    as.POSIXct("2024-08-02 20:47:03.123", tz = "UTC")
+  )
+})
+
+test_that("capture fractional seconds (issue #44)", {
+  # This test uses unclass() and %% to work around
+  # https://github.com/r-lib/testthat/issues/1977
+  expect_equal(
+    unclass(parse_iso_8601("1970-08-03T01:02:03.123+04:15")) %% 1,
+    unclass(as.POSIXct("1970-08-02 20:47:03.123", tz = "UTC")) %% 1
+  )
+
+  # Test all fractional date/time parts without explicit time zones
+  expect_equal(
+    parse_iso_8601("1970-08-03T01.5"),
+    as.POSIXct("1970-08-03 01:30", tz = "UTC")
+  )
+  expect_equal(
+    parse_iso_8601("1970-08-03T01:02.5"),
+    as.POSIXct("1970-08-03 01:02:30", tz = "UTC")
+  )
+  expect_equal(
+    unclass(parse_iso_8601("1970-08-03T01:02:03.5")) %% 1,
+    unclass(as.POSIXct("1970-08-03 01:02:30.5", tz = "UTC")) %% 1
+  )
+})
diff --git a/tests/testthat/test-iso8601.r b/tests/testthat/test-iso8601.r
index aaca13d..75b33ad 100644
--- a/tests/testthat/test-iso8601.r
+++ b/tests/testthat/test-iso8601.r
@@ -57,52 +57,54 @@ test_that("Examples from moment.js", {
 test_that("Pelago examples", {
 
   tests <- read.table(stringsAsFactors = FALSE, header = FALSE,
+                      col.names = c("input", "output", "sec_frac"),
                       strip.white = TRUE, row.names = NULL, sep = "|",
                       textConnection("
-    2009-12T12:34               | 2009-12-01T12:34:00+00:00
-    2009                        | 2009-01-01T00:00:00+00:00
-    2009-05-19                  | 2009-05-19T00:00:00+00:00
-    20090519                    | 2009-05-19T00:00:00+00:00
-    2009123                     | 2009-05-03T00:00:00+00:00
-    2009-05                     | 2009-05-01T00:00:00+00:00
-    2009-123                    | 2009-05-03T00:00:00+00:00
-    2009-222                    | 2009-08-10T00:00:00+00:00
-    2009-001                    | 2009-01-01T00:00:00+00:00
-    2009-W01-1                  | 2008-12-29T00:00:00+00:00
-    2009-W51-1                  | 2009-12-14T00:00:00+00:00
-    2009-W511                   | 2009-12-14T00:00:00+00:00
-    2009-W33                    | 2009-08-10T00:00:00+00:00
-    2009W511                    | 2009-12-14T00:00:00+00:00
-    2009-05-19 00:00            | 2009-05-19T00:00:00+00:00
-    2009-05-19 14               | 2009-05-19T14:00:00+00:00
-    2009-05-19 14:31            | 2009-05-19T14:31:00+00:00
-    2009-05-19 14:39:22         | 2009-05-19T14:39:22+00:00
-    2009-05-19T14:39Z           | 2009-05-19T14:39:00+00:00
-    2009-W21-2                  | 2009-05-19T00:00:00+00:00
-    2009-W21-2T01:22            | 2009-05-19T01:22:00+00:00
-    2009-139                    | 2009-05-19T00:00:00+00:00
-    2009-05-19 14:39:22-06:00   | 2009-05-19T20:39:22+00:00
-    2009-05-19 14:39:22+0600    | 2009-05-19T08:39:22+00:00
-    2009-05-19 14:39:22-01      | 2009-05-19T15:39:22+00:00
-    20090621T0545Z              | 2009-06-21T05:45:00+00:00
-    2007-04-06T00:00            | 2007-04-06T00:00:00+00:00
-    2007-04-05T24:00            | 2007-04-05T00:00:00+00:00
-    2010-02-18T16:23:48.5       | 2010-02-18T16:23:48+00:00
-    2010-02-18T16:23:48,444     | 2010-02-18T16:23:48+00:00
-    2010-02-18T16:23:48,3-06:00 | 2010-02-18T22:23:48+00:00
-    2010-02-18T16:23.4          | 2010-02-18T16:23:24+00:00
-    2010-02-18T16:23,25         | 2010-02-18T16:23:15+00:00
-    2010-02-18T16:23.33+0600    | 2010-02-18T10:23:19+00:00
-    2010-02-18T16.23334444      | 2010-02-18T16:14:00+00:00
-    2010-02-18T16,2283          | 2010-02-18T16:13:41+00:00
-    2009-05-19 143922.500       | 2009-05-19T14:39:22+00:00
-    2009-05-19 1439,55          | 2009-05-19T14:39:33+00:00"
+    2009-12T12:34               | 2009-12-01T12:34:00+00:00 | 0
+    2009                        | 2009-01-01T00:00:00+00:00 | 0
+    2009-05-19                  | 2009-05-19T00:00:00+00:00 | 0
+    20090519                    | 2009-05-19T00:00:00+00:00 | 0
+    2009123                     | 2009-05-03T00:00:00+00:00 | 0
+    2009-05                     | 2009-05-01T00:00:00+00:00 | 0
+    2009-123                    | 2009-05-03T00:00:00+00:00 | 0
+    2009-222                    | 2009-08-10T00:00:00+00:00 | 0
+    2009-001                    | 2009-01-01T00:00:00+00:00 | 0
+    2009-W01-1                  | 2008-12-29T00:00:00+00:00 | 0
+    2009-W51-1                  | 2009-12-14T00:00:00+00:00 | 0
+    2009-W511                   | 2009-12-14T00:00:00+00:00 | 0
+    2009-W33                    | 2009-08-10T00:00:00+00:00 | 0
+    2009W511                    | 2009-12-14T00:00:00+00:00 | 0
+    2009-05-19 00:00            | 2009-05-19T00:00:00+00:00 | 0
+    2009-05-19 14               | 2009-05-19T14:00:00+00:00 | 0
+    2009-05-19 14:31            | 2009-05-19T14:31:00+00:00 | 0
+    2009-05-19 14:39:22         | 2009-05-19T14:39:22+00:00 | 0
+    2009-05-19T14:39Z           | 2009-05-19T14:39:00+00:00 | 0
+    2009-W21-2                  | 2009-05-19T00:00:00+00:00 | 0
+    2009-W21-2T01:22            | 2009-05-19T01:22:00+00:00 | 0
+    2009-139                    | 2009-05-19T00:00:00+00:00 | 0
+    2009-05-19 14:39:22-06:00   | 2009-05-19T20:39:22+00:00 | 0
+    2009-05-19 14:39:22+0600    | 2009-05-19T08:39:22+00:00 | 0
+    2009-05-19 14:39:22-01      | 2009-05-19T15:39:22+00:00 | 0
+    20090621T0545Z              | 2009-06-21T05:45:00+00:00 | 0
+    2007-04-06T00:00            | 2007-04-06T00:00:00+00:00 | 0
+    2007-04-05T24:00            | 2007-04-05T00:00:00+00:00 | 0
+    2010-02-18T16:23:48.5       | 2010-02-18T16:23:48+00:00 | 0.5
+    2010-02-18T16:23:48,444     | 2010-02-18T16:23:48+00:00 | 0.444
+    2010-02-18T16:23:48,3-06:00 | 2010-02-18T22:23:48+00:00 | 0.3
+    2010-02-18T16:23.4          | 2010-02-18T16:23:24+00:00 | 0
+    2010-02-18T16:23,25         | 2010-02-18T16:23:15+00:00 | 0
+    2010-02-18T16:23.33+0600    | 2010-02-18T10:23:19+00:00 | 0.8
+    2010-02-18T16.23334444      | 2010-02-18T16:14:00+00:00 | 0.04
+    2010-02-18T16,2283          | 2010-02-18T16:13:41+00:00 | 0.88
+    2009-05-19 143922.500       | 2009-05-19T14:39:22+00:00 | 0.5
+    2009-05-19 1439,55          | 2009-05-19T14:39:33+00:00 | 0"
   ))
 
-  apply(tests, 1, function(x) {
-    d <- format_iso_8601(parse_iso_8601(x[1]))
-    expect_equal(d, unname(x[2]))
-  })
+  for (current_row in seq_len(nrow(tests))) {
+    d <- parse_iso_8601(tests$input[current_row])
+    expect_equal(format_iso_8601(d), tests$output[current_row])
+    expect_equal(as.numeric(d) %% 1, tests$sec_frac[current_row] %% 1, tolerance = 0.0001)
+  }
 
 })