diff --git a/.travis.yml b/.travis.yml
index d75a189..be08357 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -1,28 +1,20 @@
-language: python
+dist: xenial
+language: minimal
 
-install:
-  - if [ "$HG_VERSION" != "dev" ];
-    then pip install -q Mercurial${HG_VERSION+==$HG_VERSION};
-    else pip install -q http://selenic.com/repo/hg/archive/tip.tar.gz;
-    fi
-  - pip install -q dulwich hg-git==0.6.1 || true
-
-before_script:
-  - hg --version || true
-  - pip show hg-git dulwich
+cache:
+  directories:
+    - $HOME/.cache/git-remote-hg
 
 script:
-  - make test
+  - ./tools/check-versions hg:$HG_VERSION
 
 matrix:
   include:
-    - env: HG_VERSION=2.9.1
-    - env: HG_VERSION=2.8.2
-    - env: HG_VERSION=2.7.2
-    - env: HG_VERSION=3.0
-    - env: HG_VERSION=3.5.2
-    - env: HG_VERSION=3.6.3
-    - env: HG_VERSION=3.7
-    - env: HG_VERSION=dev
-    - python: 2.7
-    - python: 2.6
+    - env:
+    - env: HG_VERSION=@
+    - env: HG_VERSION=5.0
+    - env: HG_VERSION=4.9
+    - env: HG_VERSION=4.8
+    - env: HG_VERSION=4.7
+    - env: HG_VERSION=4.6
+    - env: HG_VERSION=4.5
diff --git a/README.asciidoc b/README.asciidoc
index 502fead..215bb04 100644
--- a/README.asciidoc
+++ b/README.asciidoc
@@ -153,8 +153,6 @@ Limitations of the remote-helpers' framework apply. In particular, these
 commands don't work:
 
 * `git push origin :branch-to-delete`
-* `git push origin old:new` (it will push 'old') (patches available)
-* `git push --dry-run origin branch` (it will push) (patches available)
 
 ****
 Another limitation is that if `git log` reports a rename, this will not survive
diff --git a/git-remote-hg b/git-remote-hg
index 112777f..caf0d8a 100755
--- a/git-remote-hg
+++ b/git-remote-hg
@@ -73,7 +73,16 @@ def gitmode(flags):
     return 'l' in flags and '120000' or 'x' in flags and '100755' or '100644'
 
 def gittz(tz):
-    return '%+03d%02d' % (-tz / 3600, -tz % 3600 / 60)
+    sign = 1 if tz >= 0 else -1
+    hours, minutes = divmod(abs(tz), 60 * 60)
+    return '%+03d%02d' % (-sign * hours, minutes / 60)
+
+def hgtz(tz):
+    tz = int(tz)
+    sign = 1 if tz >= 0 else -1
+    hours, minutes = divmod(abs(tz), 100)
+    tz = hours * 60 * 60 + minutes * 60
+    return -sign * tz
 
 def hgmode(mode):
     m = { '100755': 'x', '120000': 'l' }
@@ -280,9 +289,7 @@ class Parser:
         if ex:
             user += ex
 
-        tz = int(tz)
-        tz = ((tz / 100) * 3600) + ((tz % 100) * 60)
-        return (user, int(date), -tz)
+        return (user, int(date), hgtz(tz))
 
 def fix_file_path(path):
     def posix_path(path):
diff --git a/test/bidi.t b/test/bidi.t
index 3228ce3..5f80d09 100755
--- a/test/bidi.t
+++ b/test/bidi.t
@@ -243,4 +243,42 @@ test_expect_success 'hg tags' '
 	test_cmp expected actual
 '
 
+test_expect_success 'test timezones' '
+	test_when_finished "rm -rf gitrepo* hgrepo*" &&
+
+	(
+	git init -q gitrepo &&
+	cd gitrepo &&
+
+	echo alpha > alpha &&
+	git add alpha &&
+	git commit -m "add alpha" --date="2007-01-01 00:00:00 +0000" &&
+
+	echo beta > beta &&
+	git add beta &&
+	git commit -m "add beta" --date="2007-01-01 00:00:00 +0100" &&
+
+	echo gamma > gamma &&
+	git add gamma &&
+	git commit -m "add gamma" --date="2007-01-01 00:00:00 -0100" &&
+
+	echo delta > delta &&
+	git add delta &&
+	git commit -m "add delta" --date="2007-01-01 00:00:00 +0130" &&
+
+	echo epsilon > epsilon &&
+	git add epsilon &&
+	git commit -m "add epsilon" --date="2007-01-01 00:00:00 -0130"
+	) &&
+
+	hg_clone gitrepo hgrepo &&
+	git_clone hgrepo gitrepo2 &&
+	hg_clone gitrepo2 hgrepo2 &&
+
+	hg_log hgrepo > expected &&
+	hg_log hgrepo2 > actual &&
+
+	test_cmp expected actual
+'
+
 test_done
diff --git a/test/main.t b/test/main.t
index 2531ea8..43577ca 100755
--- a/test/main.t
+++ b/test/main.t
@@ -1050,7 +1050,7 @@ test_expect_success 'push bookmark without changesets' '
 	check_bookmark hgrepo feature-a two
 '
 
-test_expect_success 'pull tags' '
+test_expect_unstable 'pull tags' '
 	test_when_finished "rm -rf hgrepo gitrepo" &&
 
 	(
@@ -1271,6 +1271,27 @@ test_expect_success 'push annotated tag' '
 	test_cmp expected actual
 '
 
+test_expect_success 'timezone issues with negative offsets' '
+	test_when_finished "rm -rf hgrepo gitrepo1 gitrepo2" &&
+
+	hg init hgrepo &&
+
+	(
+	git clone "hg::hgrepo" gitrepo1 &&
+	cd gitrepo1 &&
+	echo two >> content &&
+	git add content &&
+	git commit -m two --date="2016-09-26 00:00:00 -0230" &&
+	git push
+	) &&
+
+	git clone "hg::hgrepo" gitrepo2 &&
+
+	git --git-dir=gitrepo1/.git log -1 --format="%ai" > expected &&
+	git --git-dir=gitrepo2/.git log -1 --format="%ai" > actual &&
+	test_cmp expected actual
+'
+
 if test "$CAPABILITY_PUSH" != "t"
 then
 test_done
diff --git a/tools/.gitignore b/tools/.gitignore
new file mode 100644
index 0000000..e2b3ee7
--- /dev/null
+++ b/tools/.gitignore
@@ -0,0 +1 @@
+results.txt
diff --git a/tools/check-versions b/tools/check-versions
new file mode 100755
index 0000000..95b891b
--- /dev/null
+++ b/tools/check-versions
@@ -0,0 +1,297 @@
+#!/usr/bin/env ruby
+
+#
+# Copyright (c) 2019 Felipe Contreras
+#
+# This script runs the tests for all versions of the components:
+#   hg, hggit and dulwich
+#
+# You can run it without arguments, in which case it reads the file
+# 'versions.txt' and executes all those checks.
+#
+# Or you can pass the versions to check manually, like:
+#
+#   ./check-versions hg:4.7 hggit:0.8.12 dulwich:0.19.7
+#
+# Or you can pass just the hg version, the other versions are fetched from
+# 'versions.txt':
+#
+#   ./check-versions hg:5.0
+#
+
+require 'fileutils'
+
+$tests = %w[main.t bidi.t hg-git.t]
+$workdir = "#{Dir.home}/.cache/git-remote-hg"
+$builddir = "/tmp/git-remote-hg-build"
+$testoutdir = "/tmp/git-remote-hg-tests"
+
+QUIET, LOW, HIGH = (1..3).to_a
+$verbosity = LOW
+
+# Util {{{1
+
+def section(text)
+  puts [nil, text, '=' * text.size]
+end
+
+def title(text)
+  puts [nil, text, '-' * text.size] unless $verbosity < HIGH
+end
+
+def run_cmd(cmd, fatal: true)
+  puts cmd.join(' ') unless $verbosity < HIGH
+  result = system(*cmd)
+  unless result or not fatal
+    STDERR.puts "Failed to run command '%s'" % cmd.join(' ')
+    exit -1
+  end
+  result
+end
+
+def check_version(a, b)
+  return true if a == '@'
+  a = a.split('.').map(&:to_i)
+  b = b.split('.').map(&:to_i)
+  (a <=> b) >= 0
+end
+
+# Component {{{1
+
+class Component
+
+  attr_reader :id
+
+  def initialize(id, url, kind: nil, **args)
+    @id = id
+    @url = url
+    @kind = kind || (url.start_with?('git') ? :git : :hg)
+    @tool = @kind.to_s
+    @checkout_fix = args[:checkout_fix]
+    @version_format = args[:version_format]
+  end
+
+  def dir
+    "#{$workdir}/#{@id}"
+  end
+
+  def get_version(version)
+    return @kind == :hg ? 'tip' : '@' if version == '@'
+    @version_format ? @version_format % version : version
+  end
+
+  def clone
+    run_cmd [@tool, 'clone', '-q', @url, dir]
+  end
+
+  def checkout(version)
+    Dir.chdir(dir) do
+      case @kind
+      when :hg
+        cmd = %w[update --clean]
+      when :git
+        cmd = %w[reset --hard]
+      else
+        cmd = %w[checkout]
+      end
+      run_cmd [@tool] + cmd + ['-q', get_version(version)]
+      @checkout_fix.call(version) if @checkout_fix
+    end
+  end
+
+  def build
+    Dir.chdir(dir) do
+      targets = %w[build_py build_ext].map { |e| [e, '--build-lib', "#{$builddir}/python"] }
+      run_cmd %w[python2 setup.py --quiet] + targets.flatten
+    end
+  end
+
+end
+
+# Functions {{{1
+
+def setup
+  dirs = %w[bin python]
+  FileUtils.mkdir_p(dirs.map { |e| "#{$builddir}/#{e}" })
+  FileUtils.mkdir_p($workdir)
+
+  $components.each do |id, component|
+    next if File.exists?(component.dir)
+
+    if $verbosity < HIGH
+      puts "Cloning #{component.id}"
+    else
+      title "Cloning #{component.id}"
+    end
+    component.clone
+  end
+end
+
+def test_env(paths: nil)
+  old = ENV.to_h
+  paths.each do |id, path|
+    name = id.to_s
+    ENV[name] = "#{path}:#{ENV[name]}"
+  end
+  r = yield
+  ENV.replace(old)
+  return r
+end
+
+def run_tests(tests)
+  title "Running tests"
+
+  Dir.chdir("#{__dir__}/../test") do
+    case $verbosity
+    when QUIET
+      tests_opt = tests.join(' ')
+      cmd = "prove -q #{tests_opt} :: -i"
+    when LOW
+      tests_opt = "T='%s'" % tests.join(' ')
+      cmd = "make -j1 #{tests_opt}"
+    else
+      tests_opt = "T='%s'" % tests.join(' ')
+      cmd = "TEST_OPTS='-v -i' make -j1 #{tests_opt}"
+    end
+    system(cmd)
+  end
+end
+
+def versions_to_s(versions)
+  versions.map { |k,v| "#{k}:#{v}" }.join(' ')
+end
+
+def versions_from_args(args)
+  args.map { |e| k, v = e.split(':'); [k.to_sym, v] }.to_h
+end
+
+def versions_from_s(str)
+  versions_from_args(str.split(' '))
+end
+
+def check(versions)
+  section versions_to_s(versions)
+
+  versions.each do |id, version|
+    component = $components[id]
+    next unless component
+
+    title "Checking out #{component.id} #{version}"
+    component.checkout(version)
+
+    title "Building #{component.id}"
+    component.build
+  end
+
+  paths = {
+    PATH: "#{$builddir}/bin",
+    PYTHONPATH: "#{$builddir}/python",
+  }
+
+  test_env(paths: paths) do
+    ENV['SHARNESS_TEST_OUTPUT_DIRECTORY'] = $testoutdir
+    run_tests($tests)
+  end
+end
+
+# Add components {{{1
+
+$components = {}
+
+def add_component(id, url, **args)
+  $components[id] = Component.new(id, url, **args)
+end
+
+hg_checkout_fix = lambda do |version|
+  FileUtils.cp('hg', "#{$builddir}/bin/")
+
+  return if check_version(version, '4.3')
+
+  if run_cmd %W[hg import -q --no-commit #{__dir__}/hg_setup_hack_2.4.patch], fatal: false
+    File.write('.hg_force_version', "%s\n" % version)
+  else
+    File.write('mercurial/__version__.py', "version = \"%s\"\n" % version)
+  end
+end
+
+add_component(:hg, 'https://www.mercurial-scm.org/repo/hg', checkout_fix: hg_checkout_fix)
+
+hggit_checkout_fix = lambda do |version|
+  return unless check_version(version, '0.8.0')
+
+  run_cmd %W[hg import -q --no-commit #{__dir__}/hggit_rename_fix_0.8.0.patch], fatal: false
+end
+
+add_component(:hggit, 'https://bitbucket.org/durin42/hg-git', checkout_fix: hggit_checkout_fix)
+
+add_component(:dulwich, 'https://github.com/dulwich/dulwich.git', version_format: 'dulwich-%s', kind: :git)
+
+def load_checks(file)
+  file.each do |e|
+    e.chomp!
+    next if e.empty? or e.start_with?('#')
+    content, comment = e.split(' # ')
+    versions = versions_from_s(content)
+    $checks << versions
+  end
+end
+
+def store_results(file)
+  $results.each do |versions, result|
+    content = versions_to_s(versions)
+    comment = result ? 'OK' : 'FAIL'
+    file.puts '%s # %s' % [content, comment]
+  end
+end
+
+# Main {{{1
+
+setup
+
+$checks = []
+$results = []
+
+$versions = versions_from_args(ARGV)
+
+File.open("#{__dir__}/versions.txt") do |f|
+  load_checks(f)
+end
+
+if $versions.size == 1 and $versions.key?(:hg)
+  # mode 1
+  $verbosity = LOW
+
+  if ['@', nil].include?($versions[:hg])
+    versions = $checks.last
+    versions[:hg] = $versions[:hg] if $versions[:hg]
+  else
+    versions = $checks.find { |e| e[:hg] == $versions[:hg] }
+    exit 1 unless versions
+  end
+
+  exit check(versions) ? 0 : 1
+elsif not $versions.empty?
+  # mode 2
+  $verbosity = HIGH
+
+  exit check(versions) ? 0 : 1
+else
+  # mode 3
+  $verbosity = QUIET
+
+  at_exit do
+    File.open("#{__dir__}/results.txt", 'w') do |f|
+      store_results(f)
+    end
+  end
+
+  failures = 0
+
+  $checks.each do |versions|
+    result = check(versions)
+    failures += 1 unless result
+    $results << [versions, result]
+  end
+
+  exit 1 unless failures == 0
+end
diff --git a/tools/hg_setup_hack_2.4.patch b/tools/hg_setup_hack_2.4.patch
new file mode 100644
index 0000000..3966daf
--- /dev/null
+++ b/tools/hg_setup_hack_2.4.patch
@@ -0,0 +1,15 @@
+diff --git a/setup.py b/setup.py
+--- a/setup.py
++++ b/setup.py
+@@ -181,7 +181,10 @@
+     # error 0xc0150004. See: http://bugs.python.org/issue3440
+     env['SystemRoot'] = os.environ['SystemRoot']
+ 
+-if os.path.isdir('.hg'):
++if os.path.exists('.hg_force_version'):
++    with open('.hg_force_version') as f:
++        version = f.read().rstrip('\n')
++elif os.path.isdir('.hg'):
+     cmd = [sys.executable, 'hg', 'log', '-r', '.', '--template', '{tags}\n']
+     numerictags = [t for t in runhg(cmd, env).split() if t[0].isdigit()]
+     hgid = runhg([sys.executable, 'hg', 'id', '-i'], env).strip()
diff --git a/tools/hggit_rename_fix_0.8.0.patch b/tools/hggit_rename_fix_0.8.0.patch
new file mode 100644
index 0000000..71ca694
--- /dev/null
+++ b/tools/hggit_rename_fix_0.8.0.patch
@@ -0,0 +1,22 @@
+diff --git a/hggit/git_handler.py b/hggit/git_handler.py
+--- a/hggit/git_handler.py
++++ b/hggit/git_handler.py
+@@ -693,6 +693,8 @@
+     def import_git_commit(self, commit):
+         self.ui.debug(_("importing: %s\n") % commit.id)
+ 
++        extra_in_message = self.ui.configbool('git', 'debugextrainmessage', False)
++
+         detect_renames = False
+         (strip_message, hg_renames,
+          hg_branch, extra) = git2hg.extract_hg_metadata(
+@@ -703,7 +705,8 @@
+             # renames detected from Git. This is because we export an extra
+             # 'HG:rename-source' Git parameter when this isn't set, which will
+             # break bidirectionality.
+-            extra['hg-git-rename-source'] = 'git'
++            if not extra_in_message:
++                extra['hg-git-rename-source'] = 'git'
+         else:
+             renames = hg_renames
+ 
diff --git a/tools/versions.txt b/tools/versions.txt
new file mode 100644
index 0000000..d410ac9
--- /dev/null
+++ b/tools/versions.txt
@@ -0,0 +1,33 @@
+# vi: ft=ruby
+
+hg:2.4 hggit:0.4.0 dulwich:0.9.0 # 2013_02
+hg:2.5 hggit:0.4.0 dulwich:0.9.0 # 2013_02
+hg:2.6 hggit:0.4.0 dulwich:0.9.0 # 2013_02
+hg:2.7 hggit:0.4.0 dulwich:0.9.0 # 2013_02
+hg:2.8 hggit:0.4.0 dulwich:0.9.0 # 2013_02
+hg:2.9 hggit:0.4.0 dulwich:0.9.0 # 2013_02
+
+hg:3.0 hggit:0.7.0 dulwich:0.10.0 # 2014_11
+hg:3.1 hggit:0.7.0 dulwich:0.10.0 # 2014_11
+hg:3.2 hggit:0.7.0 dulwich:0.10.0 # 2014_11
+
+hg:3.3 hggit:0.8.4 dulwich:0.13.0 # 2016_01
+hg:3.4 hggit:0.8.4 dulwich:0.13.0 # 2016_01
+hg:3.5 hggit:0.8.4 dulwich:0.13.0 # 2016_01
+hg:3.6 hggit:0.8.4 dulwich:0.13.0 # 2016_01
+hg:3.7 hggit:0.8.4 dulwich:0.13.0 # 2016_01
+hg:3.8 hggit:0.8.4 dulwich:0.13.0 # 2016_01
+hg:3.9 hggit:0.8.4 dulwich:0.13.0 # 2016_01
+
+hg:4.0 hggit:0.8.10 dulwich:0.18.0 # 2017_11
+hg:4.1 hggit:0.8.10 dulwich:0.18.0 # 2017_11
+hg:4.2 hggit:0.8.10 dulwich:0.18.0 # 2017_11
+hg:4.3 hggit:0.8.10 dulwich:0.18.0 # 2017_11
+hg:4.4 hggit:0.8.10 dulwich:0.18.0 # 2017_11
+
+hg:4.5 hggit:0.8.11 dulwich:0.18.0 # 2018_02
+hg:4.6 hggit:0.8.12 dulwich:0.19.7 # 2018_10
+hg:4.7 hggit:0.8.12 dulwich:0.19.7 # 2018_10
+hg:4.8 hggit:@ dulwich:0.19.11
+hg:4.9 hggit:@ dulwich:0.19.11
+hg:5.0 hggit:@ dulwich:0.19.11