diff --git a/pngpread.c b/pngpread.c
index 0a3e822cf..37aa432ae 100644
--- a/pngpread.c
+++ b/pngpread.c
@@ -229,6 +229,14 @@ png_push_read_chunk(png_structrp png_ptr, png_inforp info_ptr)
          png_benign_error(png_ptr, "Too many IDATs found");
    }
 
+   else if ((png_ptr->mode & PNG_HAVE_IDAT) != 0)
+   {
+      /* These flags must be set consistently for all non-IDAT chunks,
+       * including the unknown chunks.
+       */
+      png_ptr->mode |= PNG_HAVE_CHUNK_AFTER_IDAT | PNG_AFTER_IDAT;
+   }
+
    if (chunk_name == png_IHDR)
    {
       if (png_ptr->push_length != 13)
diff --git a/pngread.c b/pngread.c
index a0dbf2ae2..212afb7d2 100644
--- a/pngread.c
+++ b/pngread.c
@@ -702,7 +702,12 @@ png_read_end(png_structrp png_ptr, png_inforp info_ptr)
       png_uint_32 chunk_name = png_ptr->chunk_name;
 
       if (chunk_name != png_IDAT)
-         png_ptr->mode |= PNG_HAVE_CHUNK_AFTER_IDAT;
+      {
+         /* These flags must be set consistently for all non-IDAT chunks,
+          * including the unknown chunks.
+          */
+         png_ptr->mode |= PNG_HAVE_CHUNK_AFTER_IDAT | PNG_AFTER_IDAT;
+      }
 
       if (chunk_name == png_IEND)
          png_handle_chunk(png_ptr, info_ptr, length);
diff --git a/pngrutil.c b/pngrutil.c
index 7d9a00186..e7c7bbe48 100644
--- a/pngrutil.c
+++ b/pngrutil.c
@@ -2412,10 +2412,6 @@ png_handle_tEXt(png_structrp png_ptr, png_inforp info_ptr, png_uint_32 length)
    }
 #endif
 
-   /* TODO: this doesn't work and shouldn't be necessary. */
-   if ((png_ptr->mode & PNG_HAVE_IDAT) != 0)
-      png_ptr->mode |= PNG_AFTER_IDAT;
-
    buffer = png_read_buffer(png_ptr, length+1);
 
    if (buffer == NULL)
@@ -2486,10 +2482,6 @@ png_handle_zTXt(png_structrp png_ptr, png_inforp info_ptr, png_uint_32 length)
    }
 #endif
 
-   /* TODO: should not be necessary. */
-   if ((png_ptr->mode & PNG_HAVE_IDAT) != 0)
-      png_ptr->mode |= PNG_AFTER_IDAT;
-
    /* Note, "length" is sufficient here; we won't be adding
     * a null terminator later.  The limit check in png_handle_chunk should be
     * sufficient.
@@ -2606,10 +2598,6 @@ png_handle_iTXt(png_structrp png_ptr, png_inforp info_ptr, png_uint_32 length)
    }
 #endif
 
-   /* TODO: should not be necessary. */
-   if ((png_ptr->mode & PNG_HAVE_IDAT) != 0)
-      png_ptr->mode |= PNG_AFTER_IDAT;
-
    buffer = png_read_buffer(png_ptr, length+1);
 
    if (buffer == NULL)