diff --git a/qiskit/circuit/quantumcircuit.py b/qiskit/circuit/quantumcircuit.py
index 2ca6e5ead696..f50db1d96c28 100644
--- a/qiskit/circuit/quantumcircuit.py
+++ b/qiskit/circuit/quantumcircuit.py
@@ -863,16 +863,14 @@ def compose(
             mapped_instrs.append((n_instr, n_qargs, n_cargs))
 
         if front:
+            # adjust new instrs before original ones and update all parameters
             dest._data = mapped_instrs + dest._data
-        else:
-            dest._data += mapped_instrs
-
-        if front:
             dest._parameter_table.clear()
             for instr, _, _ in dest._data:
                 dest._update_parameter_table(instr)
         else:
-            # just append new parameters
+            # just append new instrs and parameters
+            dest._data += mapped_instrs
             for instr, _, _ in mapped_instrs:
                 dest._update_parameter_table(instr)