diff --git a/modules/juce_opengl/native/juce_MissingGLDefinitions.h b/modules/juce_opengl/native/juce_MissingGLDefinitions.h
index dac8bff321..ea9fe3c67a 100644
--- a/modules/juce_opengl/native/juce_MissingGLDefinitions.h
+++ b/modules/juce_opengl/native/juce_MissingGLDefinitions.h
@@ -92,6 +92,10 @@ enum MissingOpenGLDefinitions
     GL_MULTISAMPLE                  = 0x809D,
    #endif
 
+   #ifndef GL_MAX_ELEMENTS_INDICES
+    GL_MAX_ELEMENTS_INDICES         = 0x80E9,
+   #endif
+
    #if JUCE_WINDOWS && ! defined (GL_TEXTURE0)
     GL_OPERAND0_RGB                 = 0x8590,
     GL_OPERAND1_RGB                 = 0x8591,
diff --git a/modules/juce_opengl/opengl/juce_OpenGLGraphicsContext.cpp b/modules/juce_opengl/opengl/juce_OpenGLGraphicsContext.cpp
index a9b883ee02..25ebc578fc 100644
--- a/modules/juce_opengl/opengl/juce_OpenGLGraphicsContext.cpp
+++ b/modules/juce_opengl/opengl/juce_OpenGLGraphicsContext.cpp
@@ -1171,6 +1171,15 @@ struct StateHelpers
         {
             JUCE_CHECK_OPENGL_ERROR
 
+           #if JUCE_ANDROID || JUCE_IOS
+            int numQuads = maxNumQuads;
+           #else
+            GLint maxIndices = 0;
+            glGetIntegerv (GL_MAX_ELEMENTS_INDICES, &maxIndices);
+            auto numQuads = jmin ((int) maxNumQuads, (int) maxIndices / 6);
+            maxVertices = numQuads * 4 - 4;
+           #endif
+
             for (int i = 0, v = 0; i < numQuads * 6; i += 6, v += 4)
             {
                 indexData[i] = (GLushort) v;
@@ -1212,7 +1221,7 @@ struct StateHelpers
 
             numVertices += 4;
 
-            if (numVertices > numQuads * 4 - 4)
+            if (numVertices > maxVertices)
                 draw();
         }
 
@@ -1264,14 +1273,20 @@ struct StateHelpers
             GLuint colour;
         };
 
-        enum { numQuads = 256 };
+        enum { maxNumQuads = 256 };
 
         GLuint buffers[2];
-        VertexInfo vertexData[numQuads * 4];
-        GLushort indexData[numQuads * 6];
+        VertexInfo vertexData[maxNumQuads * 4];
+        GLushort indexData[maxNumQuads * 6];
         const OpenGLContext& context;
         int numVertices = 0;
 
+       #if JUCE_ANDROID || JUCE_IOS
+        enum { maxVertices = maxNumQuads * 4 - 4 };
+       #else
+        int maxVertices = 0;
+       #endif
+
         void draw() noexcept
         {
             context.extensions.glBufferSubData (GL_ARRAY_BUFFER, 0, (GLsizeiptr) ((size_t) numVertices * sizeof (VertexInfo)), vertexData);