diff --git a/cube.c b/cube.c
index 32b7343..21df46d 100644
--- a/cube.c
+++ b/cube.c
@@ -542,12 +542,36 @@ static const char *validate_params(const game_params *params, bool full)
     if (params->solid < 0 || params->solid >= lenof(solids))
 	return "Unrecognised solid type";
 
+    if (params->d1 < 0 || params->d2 < 0)
+        return "Grid dimensions may not be negative";
+
     if (solids[params->solid]->order == 4) {
 	if (params->d1 <= 1 || params->d2 <= 1)
 	    return "Both grid dimensions must be greater than one";
+        if (params->d2 > INT_MAX / params->d1)
+	    return "Grid area must not be unreasonably large";
     } else {
 	if (params->d1 <= 0 && params->d2 <= 0)
 	    return "At least one grid dimension must be greater than zero";
+
+        /*
+         * Check whether d1^2 + d2^2 + 4 d1 d2 > INT_MAX, without overflow:
+         *
+         * First check d1^2 doesn't overflow by itself.
+         *
+         * Then check d2^2 doesn't exceed the remaining space between
+         * d1^2 and INT_MAX.
+         *
+         * If that's all OK then we know both d1 and d2 are
+         * individually less than the square root of INT_MAX, so we
+         * can safely multiply them and compare against the
+         * _remaining_ space.
+         */
+        if ((params->d1 > INT_MAX / params->d1) ||
+            (params->d2 > (INT_MAX - params->d1*params->d1) / params->d2) ||
+            (params->d1*params->d2 > (INT_MAX - params->d1*params->d1 -
+                                      params->d2*params->d2) / params->d2))
+	    return "Grid area must not be unreasonably large";
     }
 
     for (i = 0; i < 4; i++)
diff --git a/filling.c b/filling.c
index 92939a1..7dec656 100644
--- a/filling.c
+++ b/filling.c
@@ -188,6 +188,8 @@ static const char *validate_params(const game_params *params, bool full)
 {
     if (params->w < 1) return "Width must be at least one";
     if (params->h < 1) return "Height must be at least one";
+    if (params->w > INT_MAX / params->h)
+        return "Width times height must not be unreasonably large";
 
     return NULL;
 }
diff --git a/range.c b/range.c
index d6d17eb..a845b82 100644
--- a/range.c
+++ b/range.c
@@ -911,8 +911,8 @@ static const char *validate_params(const game_params *params, bool full)
     int const w = params->w, h = params->h;
     if (w < 1) return "Error: width is less than 1";
     if (h < 1) return "Error: height is less than 1";
+    if (w > SCHAR_MAX - (h - 1)) return "Error: w + h is too big";
     if (w * h < 1) return "Error: size is less than 1";
-    if (w + h - 1 > SCHAR_MAX) return "Error: w + h is too big";
     /* I might be unable to store clues in my puzzle_size *grid; */
     if (full) {
         if (w == 2 && h == 2) return "Error: can't create 2x2 puzzles";
diff --git a/rect.c b/rect.c
index e2141fd..5115018 100644
--- a/rect.c
+++ b/rect.c
@@ -218,6 +218,8 @@ static const char *validate_params(const game_params *params, bool full)
 {
     if (params->w <= 0 || params->h <= 0)
 	return "Width and height must both be greater than zero";
+    if (params->w > INT_MAX / params->h)
+        return "Width times height must not be unreasonably large";
     if (params->w*params->h < 2)
 	return "Grid area must be greater than one";
     if (params->expandfactor < 0.0F)
diff --git a/slant.c b/slant.c
index 25af496..f7070d7 100644
--- a/slant.c
+++ b/slant.c
@@ -226,6 +226,8 @@ static const char *validate_params(const game_params *params, bool full)
 
     if (params->w < 2 || params->h < 2)
 	return "Width and height must both be at least two";
+    if (params->w > INT_MAX / params->h)
+        return "Width times height must not be unreasonably large";
 
     return NULL;
 }
diff --git a/unruly.c b/unruly.c
index 7a5512e..0a9403e 100644
--- a/unruly.c
+++ b/unruly.c
@@ -286,6 +286,8 @@ static const char *validate_params(const game_params *params, bool full)
         return "Width and height must both be even";
     if (params->w2 < 6 || params->h2 < 6)
         return "Width and height must be at least 6";
+    if (params->w2 > INT_MAX / params->h2)
+        return "Width times height must not be unreasonably large";
     if (params->unique) {
         static const long A177790[] = {
             /*