diff --git a/callgrind/bbcc.c b/callgrind/bbcc.c
index 36b2300e1..737f129b8 100644
--- a/callgrind/bbcc.c
+++ b/callgrind/bbcc.c
@@ -513,6 +513,13 @@ static void handleUnderflow(BB* bb)
   CLG_(current_fn_stack).top--;
   CLG_(current_state).cxt = 0;
   caller = CLG_(get_fn_node)(bb);
+
+  /* A (sentinel): if the fn we'd return into is itself skipped, push
+   * the (skipped) sentinel instead so the skipped fn doesn't surface
+   * as its own fn= block in the dump. */
+  if (caller->skip)
+    caller = CLG_(get_skipped_sentinel)();
+
   CLG_(push_cxt)( caller );
 
   if (!seen_before) {
@@ -725,7 +732,11 @@ void CLG_(setup_bbcc)(BB* bb)
     }
   }
 
-  if (jmpkind == jk_Call) {
+  /* Check obj-skip on every BB entry, not only jk_Call.
+   * The interpreter / perf trampoline can enter functions via jk_Jump
+   * or fall-through; if we only checked on jk_Call, skip would never
+   * latch for those fns and they'd leak into the dump. */
+  {
     fn_node* node = CLG_(get_fn_node)(bb);
     skip = node->skip;
     if (!skip && !node->obj_skip_checked){
@@ -794,9 +805,22 @@ void CLG_(setup_bbcc)(BB* bb)
     }
   }
   
-  /* Change new context if needed, taking delayed_push into account */
+  /* Change new context if needed, taking delayed_push into account.
+   *
+   * The `cxt == 0` clause used to fire regardless of skip, which meant
+   * that on the first BB after instrumentation start / call-stack
+   * underflow, a skipped libpython fn would still be pushed as the new
+   * top context and appear as its own fn= block in the dump.
+   *
+   * Now: if the fn is skip, we substitute the skipped sentinel so the
+   * skipped fn doesn't appear as its own fn= block in the dump. */
   if ((delayed_push && !skip) || (CLG_(current_state).cxt == 0)) {
-    CLG_(push_cxt)(CLG_(get_fn_node)(bb));
+    fn_node* push_fn = CLG_(get_fn_node)(bb);
+    /* A (sentinel): substitute the (skipped) sentinel so the
+     * skipped fn doesn't appear as its own fn= block in the dump. */
+    if (skip && CLG_(current_state).cxt == 0)
+      push_fn = CLG_(get_skipped_sentinel)();
+    CLG_(push_cxt)(push_fn);
   }
   CLG_ASSERT(CLG_(current_fn_stack).top > CLG_(current_fn_stack).bottom);
   
diff --git a/callgrind/dump.c b/callgrind/dump.c
index 3a3164c4b..4fee29af2 100644
--- a/callgrind/dump.c
+++ b/callgrind/dump.c
@@ -1553,7 +1553,17 @@ static void print_bbccs_of_thread(thread_info* ti)
     }
     
     if (*p == 0) break;
-    
+
+    /* Don't emit BBCCs whose top context fn is flagged for obj-skip.
+     * This happens when the (cxt == 0) clause in setup_bbcc force-
+     * pushes a skipped fn (first BB after instrumentation start that
+     * landed in a skipped object). Without this filter the skipped fn
+     * leaks into the dump as a top-level fn= block. */
+    if ((*p)->cxt->fn[0]->skip) {
+      p++;
+      continue;
+    }
+
     if (print_fn_pos(print_fp, &lastFnPos, *p)) {
       
       /* new function */
diff --git a/callgrind/fn.c b/callgrind/fn.c
index efa5430de..2525063d8 100644
--- a/callgrind/fn.c
+++ b/callgrind/fn.c
@@ -307,6 +307,27 @@ void CLG_(init_obj_table)(void)
 	obj_table[i] = 0;
 }
 
+static fn_node* new_fn_node(const HChar *fnname,
+                            file_node* file, fn_node* next);
+
+/* Singleton sentinel fn_node used as a placeholder cxt when we'd
+ * otherwise be forced to push a skipped fn into an empty (cxt == 0)
+ * context. Keeping skip == False on the sentinel itself is crucial:
+ * the (cxt == 0 && skip) check that would push it must NOT recurse
+ * on the sentinel. */
+static fn_node* skipped_sentinel = NULL;
+
+fn_node* CLG_(get_skipped_sentinel)(void)
+{
+    if (skipped_sentinel) return skipped_sentinel;
+
+    obj_node* obj = CLG_(get_obj_node)(NULL);   /* anonymous "???" obj */
+    file_node* file = CLG_(get_file_node)(obj, "", "(callgrind-internal)");
+    skipped_sentinel = new_fn_node("(skipped)", file, NULL);
+    skipped_sentinel->skip = False;
+    return skipped_sentinel;
+}
+
 #define HASH_CONSTANT   256
 
 static UInt str_hash(const HChar *s, UInt table_size)
diff --git a/callgrind/global.h b/callgrind/global.h
index c2fda1cce..730e665c9 100644
--- a/callgrind/global.h
+++ b/callgrind/global.h
@@ -723,6 +723,7 @@ void CLG_(set_current_fn_array)(fn_array*);
 UInt* CLG_(get_fn_entry)(Int n);
 
 void      CLG_(init_obj_table)(void);
+fn_node*  CLG_(get_skipped_sentinel)(void);
 obj_node* CLG_(get_obj_node)(DebugInfo* si);
 file_node* CLG_(get_file_node)(obj_node*, const HChar *dirname,
                                const HChar* filename);
diff --git a/callgrind/tests/runtime_obj_skip_underflow.c b/callgrind/tests/runtime_obj_skip_underflow.c
new file mode 100644
index 000000000..ffc1e6a6f
--- /dev/null
+++ b/callgrind/tests/runtime_obj_skip_underflow.c
@@ -0,0 +1,22 @@
+/* Driver for the underflow-channel obj-skip leak reproducer. */
+
+#define _GNU_SOURCE
+#include <dlfcn.h>
+#include <stdio.h>
+#include "../callgrind.h"
+
+extern void skipme_run(int depth);
+
+int main(void)
+{
+    Dl_info info;
+    if (dladdr((void*)skipme_run, &info) == 0 || !info.dli_fname) {
+        fprintf(stderr, "dladdr failed\n");
+        return 1;
+    }
+    CALLGRIND_ADD_OBJ_SKIP(info.dli_fname);
+
+    skipme_run(5);
+
+    return 0;
+}
diff --git a/callgrind/tests/runtime_obj_skip_underflow_lib.c b/callgrind/tests/runtime_obj_skip_underflow_lib.c
new file mode 100644
index 000000000..abaf58cc6
--- /dev/null
+++ b/callgrind/tests/runtime_obj_skip_underflow_lib.c
@@ -0,0 +1,37 @@
+/* Library that triggers the call-stack-underflow leak channel in
+ * callgrind obj-skip.
+ *
+ * Setup: recursive function in the skipped lib. Main calls in with
+ * instrumentation OFF, so callgrind's call stack is never populated.
+ * At the deepest frame, instrumentation is flipped ON. Each RET on
+ * the way back then sees csp == 0, hits handleUnderflow, resets
+ * cxt = 0, and force-pushes the current fn (which lives in the
+ * skipped lib) as the new top context — leaking N times for an
+ * N-deep stack.
+ *
+ * This is the same shape as Python 3.14's interpreter dispatch
+ * leaks: deep recursive eval-loop frames where instrumentation was
+ * started somewhere down the stack and every return pops past an
+ * empty callgrind stack. */
+
+#include "../callgrind.h"
+
+volatile long sink;
+
+__attribute__((noinline))
+void skipme_recurse(int n)
+{
+    if (n == 0) {
+        CALLGRIND_START_INSTRUMENTATION;
+        return;
+    }
+    skipme_recurse(n - 1);
+    sink += n;
+}
+
+__attribute__((noinline))
+void skipme_run(int depth)
+{
+    skipme_recurse(depth);
+    CALLGRIND_STOP_INSTRUMENTATION;
+}