diff --git a/examples/DSP module plugin demo/Source/PluginProcessor.cpp b/examples/DSP module plugin demo/Source/PluginProcessor.cpp
index 389776a3c8..b05febfd4c 100644
--- a/examples/DSP module plugin demo/Source/PluginProcessor.cpp	
+++ b/examples/DSP module plugin demo/Source/PluginProcessor.cpp	
@@ -137,7 +137,7 @@ void DspModulePluginDemoAudioProcessor::process (dsp::ProcessContextReplacing<fl
     // The fast tanh can be used instead of std::tanh to reduce the CPU load
     auto waveshaperIndex = waveshaperParam->getIndex();
 
-    if (isPositiveAndBelow (waveshaperIndex, (int) numWaveShapers) )
+    if (isPositiveAndBelow (waveshaperIndex, numWaveShapers) )
     {
         waveShapers[waveshaperIndex].process (waveshaperContext);
 
diff --git a/examples/audio plugin host/Source/FilterIOConfiguration.cpp b/examples/audio plugin host/Source/FilterIOConfiguration.cpp
index eb77a538ed..cd465f7eb9 100644
--- a/examples/audio plugin host/Source/FilterIOConfiguration.cpp	
+++ b/examples/audio plugin host/Source/FilterIOConfiguration.cpp	
@@ -312,7 +312,7 @@ private:
 
                     if (selectedNumChannels != bus->getLastEnabledLayout().size())
                     {
-                        if (isPositiveAndBelow (selectedNumChannels, (int) AudioChannelSet::maxChannelsOfNamedLayout)
+                        if (isPositiveAndBelow (selectedNumChannels, AudioChannelSet::maxChannelsOfNamedLayout)
                              && bus->setCurrentLayoutWithoutEnabling (bus->supportedLayoutWithChannels (selectedNumChannels)))
                         {
                             if (auto* config = owner.getConfig (! isInput))
diff --git a/modules/juce_audio_basics/midi/juce_MidiKeyboardState.cpp b/modules/juce_audio_basics/midi/juce_MidiKeyboardState.cpp
index ad52ceb8fd..68b8db06be 100644
--- a/modules/juce_audio_basics/midi/juce_MidiKeyboardState.cpp
+++ b/modules/juce_audio_basics/midi/juce_MidiKeyboardState.cpp
@@ -44,24 +44,24 @@ bool MidiKeyboardState::isNoteOn (const int midiChannel, const int n) const noex
 {
     jassert (midiChannel >= 0 && midiChannel <= 16);
 
-    return isPositiveAndBelow (n, (int) 128)
+    return isPositiveAndBelow (n, 128)
             && (noteStates[n] & (1 << (midiChannel - 1))) != 0;
 }
 
 bool MidiKeyboardState::isNoteOnForChannels (const int midiChannelMask, const int n) const noexcept
 {
-    return isPositiveAndBelow (n, (int) 128)
+    return isPositiveAndBelow (n, 128)
             && (noteStates[n] & midiChannelMask) != 0;
 }
 
 void MidiKeyboardState::noteOn (const int midiChannel, const int midiNoteNumber, const float velocity)
 {
     jassert (midiChannel >= 0 && midiChannel <= 16);
-    jassert (isPositiveAndBelow (midiNoteNumber, (int) 128));
+    jassert (isPositiveAndBelow (midiNoteNumber, 128));
 
     const ScopedLock sl (lock);
 
-    if (isPositiveAndBelow (midiNoteNumber, (int) 128))
+    if (isPositiveAndBelow (midiNoteNumber, 128))
     {
         const int timeNow = (int) Time::getMillisecondCounter();
         eventsToAdd.addEvent (MidiMessage::noteOn (midiChannel, midiNoteNumber, velocity), timeNow);
@@ -73,7 +73,7 @@ void MidiKeyboardState::noteOn (const int midiChannel, const int midiNoteNumber,
 
 void MidiKeyboardState::noteOnInternal  (const int midiChannel, const int midiNoteNumber, const float velocity)
 {
-    if (isPositiveAndBelow (midiNoteNumber, (int) 128))
+    if (isPositiveAndBelow (midiNoteNumber, 128))
     {
         noteStates [midiNoteNumber] |= (1 << (midiChannel - 1));
 
diff --git a/modules/juce_audio_basics/midi/juce_MidiMessage.cpp b/modules/juce_audio_basics/midi/juce_MidiMessage.cpp
index bf2eb56cd3..054981cae7 100644
--- a/modules/juce_audio_basics/midi/juce_MidiMessage.cpp
+++ b/modules/juce_audio_basics/midi/juce_MidiMessage.cpp
@@ -452,8 +452,8 @@ MidiMessage MidiMessage::aftertouchChange (const int channel,
                                            const int aftertouchValue) noexcept
 {
     jassert (channel > 0 && channel <= 16); // valid channels are numbered 1 to 16
-    jassert (isPositiveAndBelow (noteNum, (int) 128));
-    jassert (isPositiveAndBelow (aftertouchValue, (int) 128));
+    jassert (isPositiveAndBelow (noteNum, 128));
+    jassert (isPositiveAndBelow (aftertouchValue, 128));
 
     return MidiMessage (MidiHelpers::initialByte (0xa0, channel),
                         noteNum & 0x7f,
@@ -474,7 +474,7 @@ int MidiMessage::getChannelPressureValue() const noexcept
 MidiMessage MidiMessage::channelPressureChange (const int channel, const int pressure) noexcept
 {
     jassert (channel > 0 && channel <= 16); // valid channels are numbered 1 to 16
-    jassert (isPositiveAndBelow (pressure, (int) 128));
+    jassert (isPositiveAndBelow (pressure, 128));
 
     return MidiMessage (MidiHelpers::initialByte (0xd0, channel), pressure & 0x7f);
 }
@@ -522,7 +522,7 @@ int MidiMessage::getPitchWheelValue() const noexcept
 MidiMessage MidiMessage::pitchWheel (const int channel, const int position) noexcept
 {
     jassert (channel > 0 && channel <= 16); // valid channels are numbered 1 to 16
-    jassert (isPositiveAndBelow (position, (int) 0x4000));
+    jassert (isPositiveAndBelow (position, 0x4000));
 
     return MidiMessage (MidiHelpers::initialByte (0xe0, channel),
                         position & 127, (position >> 7) & 127);
@@ -563,7 +563,7 @@ MidiMessage MidiMessage::controllerEvent (const int channel, const int controlle
 MidiMessage MidiMessage::noteOn (const int channel, const int noteNumber, const uint8 velocity) noexcept
 {
     jassert (channel > 0 && channel <= 16);
-    jassert (isPositiveAndBelow (noteNumber, (int) 128));
+    jassert (isPositiveAndBelow (noteNumber, 128));
 
     return MidiMessage (MidiHelpers::initialByte (0x90, channel),
                         noteNumber & 127, MidiHelpers::validVelocity (velocity));
@@ -577,7 +577,7 @@ MidiMessage MidiMessage::noteOn (const int channel, const int noteNumber, const
 MidiMessage MidiMessage::noteOff (const int channel, const int noteNumber, uint8 velocity) noexcept
 {
     jassert (channel > 0 && channel <= 16);
-    jassert (isPositiveAndBelow (noteNumber, (int) 128));
+    jassert (isPositiveAndBelow (noteNumber, 128));
 
     return MidiMessage (MidiHelpers::initialByte (0x80, channel),
                         noteNumber & 127, MidiHelpers::validVelocity (velocity));
@@ -591,7 +591,7 @@ MidiMessage MidiMessage::noteOff (const int channel, const int noteNumber, float
 MidiMessage MidiMessage::noteOff (const int channel, const int noteNumber) noexcept
 {
     jassert (channel > 0 && channel <= 16);
-    jassert (isPositiveAndBelow (noteNumber, (int) 128));
+    jassert (isPositiveAndBelow (noteNumber, 128));
 
     return MidiMessage (MidiHelpers::initialByte (0x80, channel), noteNumber & 127, 0);
 }
@@ -983,7 +983,7 @@ String MidiMessage::getMidiNoteName (int note, bool useSharps, bool includeOctav
     static const char* const sharpNoteNames[] = { "C", "C#", "D", "D#", "E", "F", "F#", "G", "G#", "A", "A#", "B" };
     static const char* const flatNoteNames[]  = { "C", "Db", "D", "Eb", "E", "F", "Gb", "G", "Ab", "A", "Bb", "B" };
 
-    if (isPositiveAndBelow (note, (int) 128))
+    if (isPositiveAndBelow (note, 128))
     {
         String s (useSharps ? sharpNoteNames [note % 12]
                             : flatNoteNames  [note % 12]);
diff --git a/modules/juce_audio_devices/native/juce_mac_CoreMidi.cpp b/modules/juce_audio_devices/native/juce_mac_CoreMidi.cpp
index cd98d478e6..9637792a76 100644
--- a/modules/juce_audio_devices/native/juce_mac_CoreMidi.cpp
+++ b/modules/juce_audio_devices/native/juce_mac_CoreMidi.cpp
@@ -347,7 +347,7 @@ MidiOutput* MidiOutput::openDevice (int index)
 {
     MidiOutput* mo = nullptr;
 
-    if (isPositiveAndBelow (index, (int) MIDIGetNumberOfDestinations()))
+    if (isPositiveAndBelow (index, MIDIGetNumberOfDestinations()))
     {
         MIDIEndpointRef endPoint = MIDIGetDestination ((ItemCount) index);
 
@@ -465,7 +465,7 @@ MidiInput* MidiInput::openDevice (int index, MidiInputCallback* callback)
     using namespace CoreMidiHelpers;
     MidiInput* newInput = nullptr;
 
-    if (isPositiveAndBelow (index, (int) MIDIGetNumberOfSources()))
+    if (isPositiveAndBelow (index, MIDIGetNumberOfSources()))
     {
         if (MIDIEndpointRef endPoint = MIDIGetSource ((ItemCount) index))
         {
diff --git a/modules/juce_audio_plugin_client/AU/juce_AU_Wrapper.mm b/modules/juce_audio_plugin_client/AU/juce_AU_Wrapper.mm
index 19b4ed209c..ce62442b92 100644
--- a/modules/juce_audio_plugin_client/AU/juce_AU_Wrapper.mm
+++ b/modules/juce_audio_plugin_client/AU/juce_AU_Wrapper.mm
@@ -1704,7 +1704,7 @@ private:
 
         for (MidiBuffer::Iterator i (midiEvents); i.getNextEvent (midiEventData, midiEventSize, midiEventPosition);)
         {
-            jassert (isPositiveAndBelow (midiEventPosition, (int) nFrames));
+            jassert (isPositiveAndBelow (midiEventPosition, nFrames));
             ignoreUnused (nFrames);
 
             dataSize += (size_t) midiEventSize;
diff --git a/modules/juce_audio_processors/format_types/juce_VSTPluginFormat.cpp b/modules/juce_audio_processors/format_types/juce_VSTPluginFormat.cpp
index 716b274016..172e348844 100644
--- a/modules/juce_audio_processors/format_types/juce_VSTPluginFormat.cpp
+++ b/modules/juce_audio_processors/format_types/juce_VSTPluginFormat.cpp
@@ -943,7 +943,7 @@ struct VSTPluginInstance     : public AudioPluginInstance,
 
     float getParameter (int index) override
     {
-        if (vstEffect != nullptr && isPositiveAndBelow (index, (int) vstEffect->numParameters))
+        if (vstEffect != nullptr && isPositiveAndBelow (index, vstEffect->numParameters))
         {
             const ScopedLock sl (lock);
             return vstEffect->getParameterValueFunction (vstEffect, index);
@@ -954,7 +954,7 @@ struct VSTPluginInstance     : public AudioPluginInstance,
 
     void setParameter (int index, float newValue) override
     {
-        if (vstEffect != nullptr && isPositiveAndBelow (index, (int) vstEffect->numParameters))
+        if (vstEffect != nullptr && isPositiveAndBelow (index, vstEffect->numParameters))
         {
             const ScopedLock sl (lock);
 
diff --git a/modules/juce_core/maths/juce_MathsFunctions.h b/modules/juce_core/maths/juce_MathsFunctions.h
index 7e6b348f8e..759b5c020d 100644
--- a/modules/juce_core/maths/juce_MathsFunctions.h
+++ b/modules/juce_core/maths/juce_MathsFunctions.h
@@ -212,9 +212,9 @@ void findMinAndMax (const Type* values, int numValues, Type& lowest, Type& highe
     @see jmin, jmax, jmap
 */
 template <typename Type>
-Type jlimit (const Type lowerLimit,
-             const Type upperLimit,
-             const Type valueToConstrain) noexcept
+Type jlimit (Type lowerLimit,
+             Type upperLimit,
+             Type valueToConstrain) noexcept
 {
     jassert (lowerLimit <= upperLimit); // if these are in the wrong order, results are unpredictable..
 
@@ -228,15 +228,15 @@ Type jlimit (const Type lowerLimit,
     @code valueToTest >= 0 && valueToTest < upperLimit
     @endcode
 */
-template <typename Type>
-bool isPositiveAndBelow (Type valueToTest, Type upperLimit) noexcept
+template <typename Type1, typename Type2>
+bool isPositiveAndBelow (Type1 valueToTest, Type2 upperLimit) noexcept
 {
-    jassert (Type() <= upperLimit); // makes no sense to call this if the upper limit is itself below zero..
-    return Type() <= valueToTest && valueToTest < upperLimit;
+    jassert (Type1() <= static_cast<Type1> (upperLimit)); // makes no sense to call this if the upper limit is itself below zero..
+    return Type1() <= valueToTest && valueToTest < static_cast<Type1> (upperLimit);
 }
 
-template <>
-inline bool isPositiveAndBelow (const int valueToTest, const int upperLimit) noexcept
+template <typename Type>
+bool isPositiveAndBelow (int valueToTest, Type upperLimit) noexcept
 {
     jassert (upperLimit >= 0); // makes no sense to call this if the upper limit is itself below zero..
     return static_cast<unsigned int> (valueToTest) < static_cast<unsigned int> (upperLimit);
@@ -247,27 +247,23 @@ inline bool isPositiveAndBelow (const int valueToTest, const int upperLimit) noe
     @code valueToTest >= 0 && valueToTest <= upperLimit
     @endcode
 */
-template <typename Type>
-bool isPositiveAndNotGreaterThan (Type valueToTest, Type upperLimit) noexcept
+template <typename Type1, typename Type2>
+bool isPositiveAndNotGreaterThan (Type1 valueToTest, Type2 upperLimit) noexcept
 {
-    jassert (Type() <= upperLimit); // makes no sense to call this if the upper limit is itself below zero..
-    return Type() <= valueToTest && valueToTest <= upperLimit;
+    jassert (Type1() <= static_cast<Type1> (upperLimit)); // makes no sense to call this if the upper limit is itself below zero..
+    return Type1() <= valueToTest && valueToTest <= static_cast<Type1> (upperLimit);
 }
 
-template <>
-inline bool isPositiveAndNotGreaterThan (const int valueToTest, const int upperLimit) noexcept
+template <typename Type>
+bool isPositiveAndNotGreaterThan (int valueToTest, Type upperLimit) noexcept
 {
     jassert (upperLimit >= 0); // makes no sense to call this if the upper limit is itself below zero..
     return static_cast<unsigned int> (valueToTest) <= static_cast<unsigned int> (upperLimit);
 }
 
 //==============================================================================
-/** Handy function to swap two values. */
-template <typename Type>
-void swapVariables (Type& variable1, Type& variable2)
-{
-    std::swap (variable1, variable2);
-}
+/** @deprecated  Just use std::swap instead! */
+JUCE_DEPRECATED_WITH_BODY (template <typename Type> void swapVariables (Type& variable1, Type& variable2), { std::swap (variable1, variable2); })
 
 /** Handy function for avoiding unused variables warning. */
 template <typename Type1>
diff --git a/modules/juce_graphics/fonts/juce_CustomTypeface.cpp b/modules/juce_graphics/fonts/juce_CustomTypeface.cpp
index acc1456aa6..5897a3753c 100644
--- a/modules/juce_graphics/fonts/juce_CustomTypeface.cpp
+++ b/modules/juce_graphics/fonts/juce_CustomTypeface.cpp
@@ -186,7 +186,7 @@ void CustomTypeface::addGlyph (const juce_wchar character, const Path& path, con
     // Check that you're not trying to add the same character twice..
     jassert (findGlyph (character, false) == nullptr);
 
-    if (isPositiveAndBelow ((int) character, (int) numElementsInArray (lookupTable)))
+    if (isPositiveAndBelow ((int) character, numElementsInArray (lookupTable)))
         lookupTable [character] = (short) glyphs.size();
 
     glyphs.add (new GlyphInfo (character, path, width));
@@ -205,7 +205,7 @@ void CustomTypeface::addKerningPair (const juce_wchar char1, const juce_wchar ch
 
 CustomTypeface::GlyphInfo* CustomTypeface::findGlyph (const juce_wchar character, const bool loadIfNeeded) noexcept
 {
-    if (isPositiveAndBelow ((int) character, (int) numElementsInArray (lookupTable)) && lookupTable [character] > 0)
+    if (isPositiveAndBelow ((int) character, numElementsInArray (lookupTable)) && lookupTable [character] > 0)
         return glyphs [(int) lookupTable [(int) character]];
 
     for (int i = 0; i < glyphs.size(); ++i)
diff --git a/modules/juce_graphics/geometry/juce_EdgeTable.cpp b/modules/juce_graphics/geometry/juce_EdgeTable.cpp
index 141613c844..bfcb7c7d96 100644
--- a/modules/juce_graphics/geometry/juce_EdgeTable.cpp
+++ b/modules/juce_graphics/geometry/juce_EdgeTable.cpp
@@ -572,7 +572,7 @@ void EdgeTable::intersectWithEdgeTableLine (const int y, const int* const otherL
             lastX = nextX;
 
             const int nextLevel = (level1 * (level2 + 1)) >> 8;
-            jassert (isPositiveAndBelow (nextLevel, (int) 256));
+            jassert (isPositiveAndBelow (nextLevel, 256));
 
             if (nextLevel != lastLevel)
             {
diff --git a/modules/juce_graphics/geometry/juce_EdgeTable.h b/modules/juce_graphics/geometry/juce_EdgeTable.h
index 76c318ed1d..5311a894e2 100644
--- a/modules/juce_graphics/geometry/juce_EdgeTable.h
+++ b/modules/juce_graphics/geometry/juce_EdgeTable.h
@@ -129,7 +129,7 @@ public:
                 while (--numPoints >= 0)
                 {
                     const int level = *++line;
-                    jassert (isPositiveAndBelow (level, (int) 256));
+                    jassert (isPositiveAndBelow (level, 256));
                     const int endX = *++line;
                     jassert (endX >= x);
                     const int endOfRun = (endX >> 8);
diff --git a/modules/juce_gui_basics/native/juce_mac_NSViewComponentPeer.mm b/modules/juce_gui_basics/native/juce_mac_NSViewComponentPeer.mm
index 1102b0c6dc..d1b39752ff 100644
--- a/modules/juce_gui_basics/native/juce_mac_NSViewComponentPeer.mm
+++ b/modules/juce_gui_basics/native/juce_mac_NSViewComponentPeer.mm
@@ -392,8 +392,8 @@ public:
     {
         NSRect viewFrame = [view frame];
 
-        if (! (isPositiveAndBelow (localPos.getX(), (int) viewFrame.size.width)
-             && isPositiveAndBelow (localPos.getY(), (int) viewFrame.size.height)))
+        if (! (isPositiveAndBelow (localPos.getX(), viewFrame.size.width)
+             && isPositiveAndBelow (localPos.getY(), viewFrame.size.height)))
             return false;
 
         if (! SystemStats::isRunningInAppExtensionSandbox())
diff --git a/modules/juce_gui_basics/native/juce_win32_Windowing.cpp b/modules/juce_gui_basics/native/juce_win32_Windowing.cpp
index cb769925fd..45c81f45d6 100644
--- a/modules/juce_gui_basics/native/juce_win32_Windowing.cpp
+++ b/modules/juce_gui_basics/native/juce_win32_Windowing.cpp
@@ -1179,8 +1179,8 @@ public:
     {
         auto r = getWindowRect (hwnd);
 
-        if (! (isPositiveAndBelow (localPos.x, (int) (r.right - r.left))
-                && isPositiveAndBelow (localPos.y, (int) (r.bottom - r.top))))
+        if (! (isPositiveAndBelow (localPos.x, r.right - r.left)
+                && isPositiveAndBelow (localPos.y, r.bottom - r.top)))
             return false;
 
         POINT p = { localPos.x + r.left + windowBorder.getLeft(),