diff --git a/extras/Introjucer/Source/Application/jucer_AppearanceSettings.cpp b/extras/Introjucer/Source/Application/jucer_AppearanceSettings.cpp
index da2e6a7fd6..6753f030a6 100644
--- a/extras/Introjucer/Source/Application/jucer_AppearanceSettings.cpp
+++ b/extras/Introjucer/Source/Application/jucer_AppearanceSettings.cpp
@@ -30,7 +30,7 @@ namespace AppearanceColours
     struct ColourInfo
     {
         const char* name;
-        uint32 colourID;
+        int colourID;
         bool mustBeOpaque;
         bool applyToEditorOnly;
     };
diff --git a/extras/Introjucer/Source/ComponentEditor/components/jucer_ComponentTypeHandler.cpp b/extras/Introjucer/Source/ComponentEditor/components/jucer_ComponentTypeHandler.cpp
index c67598b7d0..e922f0d5c7 100644
--- a/extras/Introjucer/Source/ComponentEditor/components/jucer_ComponentTypeHandler.cpp
+++ b/extras/Introjucer/Source/ComponentEditor/components/jucer_ComponentTypeHandler.cpp
@@ -200,10 +200,7 @@ bool ComponentTypeHandler::restoreFromXml (const XmlElement& xml,
         const String col (xml.getStringAttribute (colours[i]->xmlTagName, String::empty));
 
         if (col.isNotEmpty())
-        {
-            comp->setColour (colours[i]->colourId,
-                             Colour (col.getHexValue32()));
-        }
+            comp->setColour (colours[i]->colourId, Colour::fromString (col));
     }
 
     return true;
diff --git a/extras/Introjucer/Source/ComponentEditor/jucer_BinaryResources.cpp b/extras/Introjucer/Source/ComponentEditor/jucer_BinaryResources.cpp
index 40e25ca2f5..37ddf2b46b 100644
--- a/extras/Introjucer/Source/ComponentEditor/jucer_BinaryResources.cpp
+++ b/extras/Introjucer/Source/ComponentEditor/jucer_BinaryResources.cpp
@@ -263,7 +263,7 @@ void BinaryResources::loadFromCpp (const File& cppFileLocation, const String& cp
                 jassert (size < (int) out.getDataSize() && size > (int) out.getDataSize() - 2);
 
                 MemoryBlock mb (out.getData(), out.getDataSize());
-                mb.setSize (size);
+                mb.setSize ((size_t) size);
 
                 add (resourceName, originalFileName, mb);
             }
diff --git a/extras/Introjucer/Source/ComponentEditor/paintelements/jucer_FillType.h b/extras/Introjucer/Source/ComponentEditor/paintelements/jucer_FillType.h
index 0754bc6605..7d6feff19f 100644
--- a/extras/Introjucer/Source/ComponentEditor/paintelements/jucer_FillType.h
+++ b/extras/Introjucer/Source/ComponentEditor/paintelements/jucer_FillType.h
@@ -218,7 +218,7 @@ public:
             if (toks[0] == "solid")
             {
                 mode = solidColour;
-                colour = Colour (toks[1].getHexValue32());
+                colour = Colour::fromString (toks[1]);
             }
             else if (toks[0] == "linear"
                       || toks[0] == "radial")
@@ -230,8 +230,8 @@ public:
                 gradPos2 = RelativePositionedRectangle();
                 gradPos2.rect = PositionedRectangle (toks[2]);
 
-                gradCol1 = Colour (toks[3].fromFirstOccurrenceOf ("=", false, false).getHexValue32());
-                gradCol2 = Colour (toks[4].fromFirstOccurrenceOf ("=", false, false).getHexValue32());
+                gradCol1 = Colour::fromString (toks[3].fromFirstOccurrenceOf ("=", false, false));
+                gradCol2 = Colour::fromString (toks[4].fromFirstOccurrenceOf ("=", false, false));
             }
             else if (toks[0] == "image")
             {
diff --git a/extras/Introjucer/Source/Project Saving/jucer_ProjectExport_MSVC.h b/extras/Introjucer/Source/Project Saving/jucer_ProjectExport_MSVC.h
index fadbf52753..c3e60d98f3 100644
--- a/extras/Introjucer/Source/Project Saving/jucer_ProjectExport_MSVC.h	
+++ b/extras/Introjucer/Source/Project Saving/jucer_ProjectExport_MSVC.h	
@@ -434,7 +434,7 @@ protected:
             out.writeShort (1); // colour planes
             out.writeShort (32); // bits per pixel
             out.writeInt ((int) (dataBlock.getDataSize() - oldDataSize));
-            out.writeInt (dataBlockStart + oldDataSize);
+            out.writeInt (dataBlockStart + (int) oldDataSize);
         }
 
         jassert (out.getPosition() == dataBlockStart);
diff --git a/extras/Introjucer/Source/Project Saving/jucer_ProjectExport_XCode.h b/extras/Introjucer/Source/Project Saving/jucer_ProjectExport_XCode.h
index a0d399496e..1f084e1d24 100644
--- a/extras/Introjucer/Source/Project Saving/jucer_ProjectExport_XCode.h	
+++ b/extras/Introjucer/Source/Project Saving/jucer_ProjectExport_XCode.h	
@@ -428,7 +428,7 @@ private:
         pngFormat.writeImageToStream (image, pngData);
 
         out.write (type, 4);
-        out.writeIntBigEndian (8 + pngData.getDataSize());
+        out.writeIntBigEndian (8 + (int) pngData.getDataSize());
         out << pngData;
     }
 
@@ -457,7 +457,7 @@ private:
         jassert (data.getDataSize() > 0); // no suitable sized images?
 
         out.write ("icns", 4);
-        out.writeIntBigEndian (data.getDataSize() + 8);
+        out.writeIntBigEndian ((int) data.getDataSize() + 8);
         out << data;
     }
 
diff --git a/extras/Introjucer/Source/Utility/jucer_CodeHelpers.cpp b/extras/Introjucer/Source/Utility/jucer_CodeHelpers.cpp
index 504d8078f0..fd58970235 100644
--- a/extras/Introjucer/Source/Utility/jucer_CodeHelpers.cpp
+++ b/extras/Introjucer/Source/Utility/jucer_CodeHelpers.cpp
@@ -401,7 +401,7 @@ namespace CodeHelpers
     }
 
     //==============================================================================
-    static unsigned int calculateHash (const String& s, const int hashMultiplier)
+    static unsigned int calculateHash (const String& s, const unsigned int hashMultiplier)
     {
         const char* t = s.toUTF8();
         unsigned int hash = 0;
@@ -411,9 +411,9 @@ namespace CodeHelpers
         return hash;
     }
 
-    static int findBestHashMultiplier (const StringArray& strings)
+    static unsigned int findBestHashMultiplier (const StringArray& strings)
     {
-        int v = 31;
+        unsigned int v = 31;
 
         for (;;)
         {
@@ -445,19 +445,19 @@ namespace CodeHelpers
     {
         jassert (strings.size() == codeToExecute.size());
         const String indent (String::repeatedString (" ", indentLevel));
-        const int hashMultiplier = findBestHashMultiplier (strings);
+        const unsigned int hashMultiplier = findBestHashMultiplier (strings);
 
         out << indent << "unsigned int hash = 0;" << newLine
             << indent << "if (" << utf8PointerVariable << " != 0)" << newLine
             << indent << "    while (*" << utf8PointerVariable << " != 0)" << newLine
-            << indent << "        hash = " << hashMultiplier << " * hash + (unsigned int) *" << utf8PointerVariable << "++;" << newLine
+            << indent << "        hash = " << (int) hashMultiplier << " * hash + (unsigned int) *" << utf8PointerVariable << "++;" << newLine
             << newLine
             << indent << "switch (hash)" << newLine
             << indent << "{" << newLine;
 
         for (int i = 0; i < strings.size(); ++i)
         {
-            out << indent << "    case 0x" << hexString8Digits (calculateHash (strings[i], hashMultiplier))
+            out << indent << "    case 0x" << hexString8Digits ((int) calculateHash (strings[i], hashMultiplier))
                 << ":  " << codeToExecute[i] << newLine;
         }
 
diff --git a/extras/JuceDemo/Source/demos/TreeViewDemo.cpp b/extras/JuceDemo/Source/demos/TreeViewDemo.cpp
index 287b470819..552b594105 100644
--- a/extras/JuceDemo/Source/demos/TreeViewDemo.cpp
+++ b/extras/JuceDemo/Source/demos/TreeViewDemo.cpp
@@ -56,7 +56,7 @@ public:
             g.fillAll (Colours::blue.withAlpha (0.3f));
 
         // use a "colour" attribute in the xml tag for this node to set the text colour..
-        g.setColour (Colour ((uint32) xml.getStringAttribute ("colour", "ff000000").getHexValue32()));
+        g.setColour (Colour::fromString (xml.getStringAttribute ("colour", "ff000000")));
 
         g.setFont (height * 0.7f);
 
diff --git a/modules/juce_audio_formats/codecs/juce_WavAudioFormat.cpp b/modules/juce_audio_formats/codecs/juce_WavAudioFormat.cpp
index b7f1885d2a..f40e84aa06 100644
--- a/modules/juce_audio_formats/codecs/juce_WavAudioFormat.cpp
+++ b/modules/juce_audio_formats/codecs/juce_WavAudioFormat.cpp
@@ -753,7 +753,7 @@ public:
                 else if (chunkType == chunkName ("axml"))
                 {
                     MemoryBlock axml;
-                    input->readIntoMemoryBlock (axml, (size_t) length);
+                    input->readIntoMemoryBlock (axml, (ssize_t) length);
                     AXMLChunk::addToMetadata (metadataValues, axml.toString());
                 }
                 else if (chunkType == chunkName ("LIST"))
@@ -967,13 +967,10 @@ public:
             writeFailed = true;
             return false;
         }
-        else
-        {
-            bytesWritten += bytes;
-            lengthInSamples += (uint64) numSamples;
 
-            return true;
-        }
+        bytesWritten += bytes;
+        lengthInSamples += (uint64) numSamples;
+        return true;
     }
 
 private:
@@ -1107,7 +1104,7 @@ private:
         usesFloatingPointData = (bitsPerSample == 32);
     }
 
-    static int chunkSize (const MemoryBlock& data) noexcept     { return data.getSize() > 0 ? (8 + data.getSize()) : 0; }
+    static size_t chunkSize (const MemoryBlock& data) noexcept     { return data.getSize() > 0 ? (8 + data.getSize()) : 0; }
 
     void writeChunkHeader (int chunkType, int size) const
     {
diff --git a/modules/juce_core/misc/juce_Uuid.cpp b/modules/juce_core/misc/juce_Uuid.cpp
index 9df787f4a1..ce134b69b1 100644
--- a/modules/juce_core/misc/juce_Uuid.cpp
+++ b/modules/juce_core/misc/juce_Uuid.cpp
@@ -26,32 +26,13 @@
   ==============================================================================
 */
 
-namespace
-{
-    int64 getRandomSeedFromMACAddresses()
-    {
-        Array<MACAddress> result;
-        MACAddress::findAllAddresses (result);
-
-        Random r;
-        for (int i = 0; i < result.size(); ++i)
-            r.combineSeed (result[i].toInt64());
 
-        return r.nextInt64();
-    }
-}
-
-//==============================================================================
 Uuid::Uuid()
 {
-    // The normal random seeding is pretty good, but we'll throw some MAC addresses
-    // into the mix too, to make it very very unlikely that two UUIDs will ever be the same..
-
-    static Random r1 (getRandomSeedFromMACAddresses());
-    Random r2;
+    Random r;
 
     for (size_t i = 0; i < sizeof (uuid); ++i)
-        uuid[i] = (uint8) (r1.nextInt() ^ r2.nextInt());
+        uuid[i] = (uint8) (r.nextInt (256));
 }
 
 Uuid::~Uuid() noexcept {}
diff --git a/modules/juce_core/text/juce_String.cpp b/modules/juce_core/text/juce_String.cpp
index 139c2bb4b2..d62ce3b0d4 100644
--- a/modules/juce_core/text/juce_String.cpp
+++ b/modules/juce_core/text/juce_String.cpp
@@ -637,7 +637,7 @@ void String::appendCharPointer (const CharPointerType startOfTextToAppend,
         preallocateBytes (byteOffsetOfNull + (size_t) extraBytesNeeded);
 
         CharPointerType::CharType* const newStringStart = addBytesToPointer (text.getAddress(), (int) byteOffsetOfNull);
-        memcpy (newStringStart, startOfTextToAppend.getAddress(), extraBytesNeeded);
+        memcpy (newStringStart, startOfTextToAppend.getAddress(), (size_t) extraBytesNeeded);
         CharPointerType (addBytesToPointer (newStringStart, extraBytesNeeded)).writeNull();
     }
 }
diff --git a/modules/juce_graphics/geometry/juce_EdgeTable.cpp b/modules/juce_graphics/geometry/juce_EdgeTable.cpp
index 4776a639c9..c3846f582c 100644
--- a/modules/juce_graphics/geometry/juce_EdgeTable.cpp
+++ b/modules/juce_graphics/geometry/juce_EdgeTable.cpp
@@ -336,7 +336,7 @@ void EdgeTable::sanitiseLevels (const bool useNonZeroWinding) noexcept
                 if (items[i].x == items[i + 1].x)
                 {
                     items[i].level += items[i + 1].level;
-                    memmove (items + i + 1, items + i + 2, (num - i - 2) * sizeof (LineItem));
+                    memmove (items + i + 1, items + i + 2, (size_t) (num - i - 2) * sizeof (LineItem));
                     --num;
                     --lineStart[0];
                     --i;
diff --git a/modules/juce_graphics/image_formats/juce_JPEGLoader.cpp b/modules/juce_graphics/image_formats/juce_JPEGLoader.cpp
index 2d2a6a4879..5788c2c1da 100644
--- a/modules/juce_graphics/image_formats/juce_JPEGLoader.cpp
+++ b/modules/juce_graphics/image_formats/juce_JPEGLoader.cpp
@@ -166,7 +166,7 @@ namespace JPEGHelpers
         decompStruct->src->next_input_byte += num;
 
         num = jmin (num, (long) decompStruct->src->bytes_in_buffer);
-        decompStruct->src->bytes_in_buffer -= num;
+        decompStruct->src->bytes_in_buffer -= (size_t) num;
     }
 
     static boolean jpegFill (j_decompress_ptr)
diff --git a/modules/juce_graphics/image_formats/juce_PNGLoader.cpp b/modules/juce_graphics/image_formats/juce_PNGLoader.cpp
index 36fb799a1c..4ee36abaae 100644
--- a/modules/juce_graphics/image_formats/juce_PNGLoader.cpp
+++ b/modules/juce_graphics/image_formats/juce_PNGLoader.cpp
@@ -401,10 +401,10 @@ Image PNGImageFormat::decodeImage (InputStream& in)
 
             // Load the image into a temp buffer in the pnglib format..
             const size_t lineStride = width * 4;
-            HeapBlock <uint8> tempBuffer (height * lineStride);
+            HeapBlock<uint8> tempBuffer (height * lineStride);
 
-            HeapBlock <png_bytep> rows (height);
-            for (int y = (int) height; --y >= 0;)
+            HeapBlock<png_bytep> rows (height);
+            for (size_t y = 0; y < height; ++y)
                 rows[y] = (png_bytep) (tempBuffer + lineStride * y);
 
             try
diff --git a/modules/juce_graphics/native/juce_mac_CoreGraphicsContext.mm b/modules/juce_graphics/native/juce_mac_CoreGraphicsContext.mm
index 407f32f938..6bdd835697 100644
--- a/modules/juce_graphics/native/juce_mac_CoreGraphicsContext.mm
+++ b/modules/juce_graphics/native/juce_mac_CoreGraphicsContext.mm
@@ -527,7 +527,7 @@ void CoreGraphicsContext::drawLine (const Line<float>& line)
 
 void CoreGraphicsContext::fillRectList (const RectangleList<float>& list)
 {
-    HeapBlock<CGRect> rects (list.getNumRectangles());
+    HeapBlock<CGRect> rects ((size_t) list.getNumRectangles());
 
     size_t num = 0;
     for (const Rectangle<float>* r = list.begin(), * const e = list.end(); r != e; ++r)