diff --git a/doc/fixes37.0 b/doc/fixes37.0
index e21072f9d..25d694010 100644
--- a/doc/fixes37.0
+++ b/doc/fixes37.0
@@ -674,6 +674,9 @@ don't give lance or mattock as starting equipment when creating soldiers
 fixup for the insect "legs" (some extraneous walls inside solid stone) on the
 	baalz level didn't work as intended if that level was flipped
 handle flipped level when fixing up the baalz level "eyes" too
+prevent normal monster activity from picking up the mines' luckstone or the
+	Sokoban amulet/bag before hero has done so; relying on scare monster
+	and/or engraved Elbereth wasn't sufficient to guard the Sokoban prize
 
 
 Fixes to 3.7.0-x Problems that Were Exposed Via git Repository
diff --git a/src/dogmove.c b/src/dogmove.c
index 16c0b9d12..1fc4a02e0 100644
--- a/src/dogmove.c
+++ b/src/dogmove.c
@@ -441,7 +441,9 @@ dog_invent(struct monst *mtmp, struct edog *edog, int udist)
 #ifdef MAIL_STRUCTURES
             && obj->otyp != SCR_MAIL
 #endif
-            ) {
+            /* avoid special items; once hero picks them up, they'll cease
+               being special and become eligible for normal monst activity */
+            && !(is_mines_prize(obj) || is_soko_prize(obj))) {
             int edible = dogfood(mtmp, obj);
 
             if ((edible <= CADAVER
diff --git a/src/mon.c b/src/mon.c
index 40299b0db..36488ce78 100644
--- a/src/mon.c
+++ b/src/mon.c
@@ -1191,6 +1191,12 @@ meatobj(struct monst* mtmp) /* for gelatinous cubes */
     for (otmp = g.level.objects[mtmp->mx][mtmp->my]; otmp; otmp = otmp2) {
         otmp2 = otmp->nexthere;
 
+        /* avoid special items; once hero picks them up, they'll cease
+           being special, becoming eligible for engulf and devore if
+           dropped again */
+        if (is_mines_prize(otmp) || is_soko_prize(otmp))
+            continue;
+
         /* touch sensitive items */
         if (otmp->otyp == CORPSE && is_rider(&mons[otmp->corpsenm])) {
             int ox = otmp->ox, oy = otmp->oy;
@@ -1493,6 +1499,12 @@ mpickstuff(register struct monst* mtmp, register const char* str)
 
     for (otmp = g.level.objects[mtmp->mx][mtmp->my]; otmp; otmp = otmp2) {
         otmp2 = otmp->nexthere;
+
+        /* avoid special items; once hero picks them up, they'll cease
+           being special, becoming eligible for normal pickup */
+        if (is_mines_prize(otmp) || is_soko_prize(otmp))
+            continue;
+
         /* Nymphs take everything.  Most monsters don't pick up corpses. */
         if (!str ? searches_for_item(mtmp, otmp)
                  : !!(index(str, otmp->oclass))) {
diff --git a/src/monmove.c b/src/monmove.c
index b9426a444..59158224a 100644
--- a/src/monmove.c
+++ b/src/monmove.c
@@ -1184,6 +1184,11 @@ m_move(register struct monst* mtmp, register int after)
                    down on move overhead by filtering out most common item */
                 if (otmp->otyp == ROCK)
                     continue;
+                /* avoid special items; once hero picks them up, they'll
+                   cease being special */
+                if (is_mines_prize(otmp) || is_soko_prize(otmp))
+                    continue;
+
                 xx = otmp->ox;
                 yy = otmp->oy;
                 /* Nymphs take everything.  Most other creatures should not