diff --git a/.travis.yml b/.travis.yml
index 62907a985a..67c5f41e6f 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -7,42 +7,51 @@ sudo: required
 
 matrix:
     include:
-        - dist: precise
-          compiler: gcc
-          env: wxUSE_XVFB=1
-        - dist: trusty
-          compiler: gcc
-        - dist: trusty
-          compiler: gcc
-          env: wxCONFIGURE_FLAGS="--enable-utf8 --enable-utf8only --enable-monolithic" wxUSE_XVFB=1
-        - dist: trusty
-          compiler: gcc
-          env: wxGTK_VERSION=3 wxCONFIGURE_FLAGS="--enable-cxx11 --enable-stl --disable-webview" wxMAKEFILE_FLAGS="CXXFLAGS=-std=c++11" wxUSE_XVFB=1
-        - dist: trusty
-          compiler: clang
-          env: wxCONFIGURE_FLAGS="--disable-shared --disable-sys-libs --disable-webview" wxUSE_XVFB=1
-        - dist: trusty
-          compiler: gcc
-          env: wxTOOLSET=cmake wxCMAKE_GENERATOR="Unix Makefiles"
-        - os: osx
-          osx_image: xcode6.4
-          compiler: clang
-          env: wxCONFIGURE_FLAGS="--enable-cxx11" wxMAKEFILE_FLAGS="CXXFLAGS=-std=c++11" wxSKIP_SAMPLES=1
-        - os: osx
-          compiler: clang
-          env: wxTOOLSET=cmake wxCMAKE_GENERATOR=Xcode wxCMAKE_DEFINES="-DCMAKE_CXX_STANDARD=11"
-        - dist: trusty
-          compiler: gcc
-          env: wxCONFIGURE_FLAGS="--with-x11 --enable-pch --disable-stc" wxSKIP_SAMPLES=1
-        - dist: trusty
-          compiler: gcc
-          env: wxCONFIGURE_FLAGS="--with-directfb --enable-pch --disable-stc" wxSKIP_SAMPLES=1
-        - dist: trusty
-          compiler: gcc
-          env: wxCONFIGURE_FLAGS="--with-motif --enable-pch --disable-stc" wxSKIP_SAMPLES=1
-        - dist: trusty
-          compiler: gcc
-          env: wxCONFIGURE_FLAGS="--with-qt --enable-pch" wxSKIP_SAMPLES=1
+        - os: linux
+          arch: arm64
+          env: wxCONFIGURE_FLAGS="--disable-sys-libs" wxLXC=1
+        - os: linux
+          arch: ppc64le
+          env: wxCONFIGURE_FLAGS="--disable-sys-libs" wxLXC=1
+        - os: linux
+          arch: s390x
+          env: wxCONFIGURE_FLAGS="--disable-sys-libs" wxLXC=1
+#        - dist: precise
+#          compiler: gcc
+#          env: wxUSE_XVFB=1
+#        - dist: trusty
+#          compiler: gcc
+#        - dist: trusty
+#          compiler: gcc
+#          env: wxCONFIGURE_FLAGS="--enable-utf8 --enable-utf8only --enable-monolithic" wxUSE_XVFB=1
+#        - dist: trusty
+#          compiler: gcc
+#          env: wxGTK_VERSION=3 wxCONFIGURE_FLAGS="--enable-cxx11 --enable-stl --disable-webview" wxMAKEFILE_FLAGS="CXXFLAGS=-std=c++11" wxUSE_XVFB=1
+#        - dist: trusty
+#          compiler: clang
+#          env: wxCONFIGURE_FLAGS="--disable-shared --disable-sys-libs --disable-webview" wxUSE_XVFB=1
+#        - dist: trusty
+#          compiler: gcc
+#          env: wxTOOLSET=cmake wxCMAKE_GENERATOR="Unix Makefiles"
+#        - os: osx
+#          osx_image: xcode6.4
+#          compiler: clang
+#          env: wxCONFIGURE_FLAGS="--enable-cxx11" wxMAKEFILE_FLAGS="CXXFLAGS=-std=c++11" wxSKIP_SAMPLES=1
+#        - os: osx
+#          compiler: clang
+#          env: wxTOOLSET=cmake wxCMAKE_GENERATOR=Xcode wxCMAKE_DEFINES="-DCMAKE_CXX_STANDARD=11"
+#        - dist: trusty
+#          compiler: gcc
+#          env: wxCONFIGURE_FLAGS="--with-x11 --enable-pch --disable-stc" wxSKIP_SAMPLES=1
+#        - dist: trusty
+#          compiler: gcc
+#          env: wxCONFIGURE_FLAGS="--with-directfb --enable-pch --disable-stc" wxSKIP_SAMPLES=1
+#        - dist: trusty
+#          compiler: gcc
+#          env: wxCONFIGURE_FLAGS="--with-motif --enable-pch --disable-stc" wxSKIP_SAMPLES=1
+#        - dist: trusty
+#          compiler: gcc
+#          env: wxCONFIGURE_FLAGS="--with-qt --enable-pch" wxSKIP_SAMPLES=1
 
 branches:
     only:
diff --git a/tests/file/filetest.cpp b/tests/file/filetest.cpp
index f1876daf94..0f31b12db3 100644
--- a/tests/file/filetest.cpp
+++ b/tests/file/filetest.cpp
@@ -149,21 +149,26 @@ TEST_CASE("wxFile::Special", "[file][linux][special-file]")
     // for reading) and usually we don't have the permissions to do it.
 
     // This file is not seekable and has 0 size, but can still be read.
-    wxFile fileProc("/proc/diskstats");
+    wxFile fileProc("/proc/cpuinfo");
     CHECK( fileProc.IsOpened() );
 
     wxString s;
     CHECK( fileProc.ReadAll(&s) );
-    CHECK( !s.empty() );
 
-    // All files in /sys seem to have size of 4KiB currently, even if they
-    // don't have that much data in them.
+    // /proc files seem to be always empty in LXC containers.
+    if ( !IsRunningInLXC() )
+        CHECK( !s.empty() );
+
+    // All files in /sys have the size of one kernel page, even if they don't
+    // have that much data in them.
+    const long pageSize = sysconf(_SC_PAGESIZE);
+
     wxFile fileSys("/sys/power/state");
-    CHECK( fileSys.Length() == 4096 );
+    CHECK( fileSys.Length() == pageSize );
     CHECK( fileSys.IsOpened() );
     CHECK( fileSys.ReadAll(&s) );
     CHECK( !s.empty() );
-    CHECK( s.length() < 4096 );
+    CHECK( s.length() < pageSize );
 }
 
 #endif // __LINUX__
diff --git a/tests/filename/filenametest.cpp b/tests/filename/filenametest.cpp
index 240e95205c..1db0edc52d 100644
--- a/tests/filename/filenametest.cpp
+++ b/tests/filename/filenametest.cpp
@@ -1059,8 +1059,9 @@ TEST_CASE("wxFileName::GetSizeSpecial", "[filename][linux][special-file]")
     INFO( "size of /proc/kcore=" << size );
     CHECK( size > 0 );
 
-    // All files in /sys seem to have size of 4KiB currently.
-    CHECK( wxFileName::GetSize("/sys/power/state") == 4096 );
+    // All files in /sys are one page in size, irrespectively of the size of
+    // their actual contents.
+    CHECK( wxFileName::GetSize("/sys/power/state") == sysconf(_SC_PAGESIZE) );
 }
 
 #endif // __LINUX__
diff --git a/tests/test.cpp b/tests/test.cpp
index 851785a72c..259c7c71db 100644
--- a/tests/test.cpp
+++ b/tests/test.cpp
@@ -422,6 +422,20 @@ extern bool IsRunningUnderXVFB()
     return s_isRunningUnderXVFB == 1;
 }
 
+#ifdef __LINUX__
+
+extern bool IsRunningInLXC()
+{
+    // We're supposed to be able to detect running in LXC by checking for
+    // /dev/lxd existency, but this doesn't work under Travis for some reason,
+    // so just rely on having the environment variable defined for the
+    // corresponding builds in our .travis.yml.
+    wxString value;
+    return wxGetEnv("wxLXC", &value) && value == "1";
+}
+
+#endif // __LINUX__
+
 #if wxUSE_GUI
 
 bool EnableUITests()
diff --git a/tests/testprec.h b/tests/testprec.h
index 7ae35168cc..38e2ce14e0 100644
--- a/tests/testprec.h
+++ b/tests/testprec.h
@@ -123,6 +123,10 @@ extern bool IsAutomaticTest();
 
 extern bool IsRunningUnderXVFB();
 
+#ifdef __LINUX__
+extern bool IsRunningInLXC();
+#endif // __LINUX__
+
 // Helper class setting the locale to the given one for its lifetime.
 class LocaleSetter
 {
diff --git a/tests/textfile/textfiletest.cpp b/tests/textfile/textfiletest.cpp
index eda450d1f3..dc7d22423d 100644
--- a/tests/textfile/textfiletest.cpp
+++ b/tests/textfile/textfiletest.cpp
@@ -347,8 +347,12 @@ TEST_CASE("wxTextFile::Special", "[textfile][linux][special-file]")
     SECTION("/proc")
     {
         wxTextFile f;
-        CHECK( f.Open("/proc/diskstats") );
-        CHECK( f.GetLineCount() > 1 );
+        CHECK( f.Open("/proc/cpuinfo") );
+
+        // /proc files seem to be always empty in LXC containers, so skip this
+        // check there.
+        if ( !IsRunningInLXC() )
+            CHECK( f.GetLineCount() > 1 );
     }
 
     SECTION("/sys")
@@ -357,7 +361,7 @@ TEST_CASE("wxTextFile::Special", "[textfile][linux][special-file]")
         CHECK( f.Open("/sys/power/state") );
         REQUIRE( f.GetLineCount() == 1 );
         INFO( "/sys/power/state contains \"" << f[0] << "\"" );
-        CHECK( f[0].find("mem") != wxString::npos );
+        CHECK( (f[0].find("mem") != wxString::npos || f[0].find("disk") != wxString::npos) );
     }
 }