diff --git a/src/tensorfold/cuda/server.py b/src/tensorfold/cuda/server.py
index 43cbc02a69..b66c853fb5 100644
--- a/src/tensorfold/cuda/server.py
+++ b/src/tensorfold/cuda/server.py
@@ -18,6 +18,7 @@
 from tensorfold.server.messages import validate_modalities
 from tensorfold.server.plain_text import PlainText
 from tensorfold.server.probabilities import TokenBytes, probability_options
+from tensorfold.server.prompt_pieces import PromptPieces
 from tensorfold.server.request_options import heard_effort, parse_numbers, thinking_fields
 from tensorfold.server.stopping import matched_stop, stop_options
 from tensorfold.server.thinking_notes import unanswered
@@ -119,6 +120,15 @@ def _plain_text(self) -> PlainText | None:
                     self.tok, assistant_keep=self.plain_assistant_keep)
             return made
 
+    def _prompt_pieces(self) -> PromptPieces | None:
+        """The chat prompts' encoded pieces, made once; None for a tokenizer they cannot follow."""
+
+        with _MADE:
+            made = self.__dict__.get("_prompt_pieces_made")
+            if made is None:
+                made = self.__dict__["_prompt_pieces_made"] = PromptPieces.of(self.tok)
+            return made
+
     @property
     def model_ids(self) -> list[str]:
         """The ids this endpoint answers to, as the MLX server lists them: ``--name`` first, then each ``--alias``."""
@@ -322,7 +332,8 @@ def render(messages: list[dict[str, Any]], **images: bool) -> str:   # text rend
                 prompt = plain.encode(text, shield)
             else:
                 text = render(body["messages"])
-                prompt = self._encode(text, False)
+                pieces = self._prompt_pieces()
+                prompt = self._encode(text, False) if pieces is None else pieces.ids(text)
         elif isinstance(body.get("prompt"), list):       # token ids (vLLM's and OpenAI's form): served as given
             prompt = self.token_ids(body["prompt"])
         else:
diff --git a/src/tensorfold/server/prompt_pieces.py b/src/tensorfold/server/prompt_pieces.py
new file mode 100644
index 0000000000..79f00a611d
--- /dev/null
+++ b/src/tensorfold/server/prompt_pieces.py
@@ -0,0 +1,72 @@
+"""Token ids of re-sent chat prompts: each piece between added tokens is encoded once, then reused.
+
+A tokenizer splits its input at the added tokens it matches before normalization and encodes each part on its own, so
+a piece that ends in one encodes alone to the ids it gets inside the whole text. A chat client re-sends its whole
+conversation every turn; only the pieces it has not sent before need the tokenizer.
+"""
+
+from __future__ import annotations
+
+import re
+import threading
+from array import array
+from collections import OrderedDict
+from typing import Any
+
+BUDGET = 1 << 21        # tokens kept across all pieces (4 bytes each, plus the pieces' text)
+
+
+class PromptPieces:
+    """``ids(text)`` equals ``tok.encode(text, add_special_tokens=False).ids``."""
+
+    def __init__(self, tok: Any, cut: re.Pattern[str], budget: int = BUDGET) -> None:
+        self._tok, self._cut, self._budget = tok, cut, budget
+        self._kept: OrderedDict[str, array] = OrderedDict()      # least recently used first
+        self._held = 0
+        self._lock = threading.Lock()
+
+    @classmethod
+    def of(cls, tok: Any, budget: int = BUDGET) -> PromptPieces | None:
+        """Pieces for ``tok``, or None where a cut could fall where the tokenizer does not split."""
+
+        if not all(callable(getattr(tok, name, None)) for name in ("encode_batch", "get_added_tokens_decoder")):
+            return None
+        if getattr(tok, "encode_special_tokens", False):        # special tokens are encoded as text, not split out
+            return None
+        first = [token for token in tok.get_added_tokens_decoder().values() if not token.normalized]
+        # rstrip takes the spaces after a token into its match, and single_word skips a match inside a word
+        if not first or any(token.rstrip or token.single_word for token in first):
+            return None
+        spellings = sorted({token.content for token in first if token.content}, key=len, reverse=True)
+        return cls(tok, re.compile("|".join(map(re.escape, spellings))), budget)     # the longest at the leftmost
+
+    def ids(self, text: str) -> list[int]:
+        pieces, at = [], 0
+        for match in self._cut.finditer(text):
+            pieces.append(text[at:match.end()])
+            at = match.end()
+        if at < len(text):
+            pieces.append(text[at:])
+        with self._lock:
+            found = {piece: self._kept[piece] for piece in pieces if piece in self._kept}
+            for piece in found:
+                self._kept.move_to_end(piece)
+        missing = [piece for piece in dict.fromkeys(pieces) if piece not in found]
+        if missing:                       # encode_batch releases the GIL while it encodes
+            encoded = self._tok.encode_batch(missing, add_special_tokens=False)
+            new = {piece: array("I", encoding.ids) for piece, encoding in zip(missing, encoded)}
+            found.update(new)
+            self._keep(new)
+        ids: list[int] = []
+        for piece in pieces:
+            ids.extend(found[piece])
+        return ids
+
+    def _keep(self, new: dict[str, array]) -> None:
+        with self._lock:
+            for piece, ids in new.items():
+                if piece not in self._kept and len(ids) <= self._budget:
+                    self._kept[piece] = ids
+                    self._held += len(ids)
+            while self._held > self._budget:
+                self._held -= len(self._kept.popitem(last=False)[1])
diff --git a/tests/test_prompt_pieces.py b/tests/test_prompt_pieces.py
new file mode 100644
index 0000000000..819bd6f761
--- /dev/null
+++ b/tests/test_prompt_pieces.py
@@ -0,0 +1,121 @@
+"""PromptPieces: a chat prompt's ids equal the tokenizer's, and a re-sent conversation encodes only its new pieces."""
+
+import json
+import random
+from types import SimpleNamespace
+
+import pytest
+
+tokenizers = pytest.importorskip("tokenizers")
+from tokenizers import AddedToken, Regex, Tokenizer, models, normalizers, pre_tokenizers, trainers
+
+from tensorfold.server.prompt_pieces import PromptPieces
+
+TURN, END, TOOL, CALL, MARK = "<｜User｜>", "<｜end▁of▁sentence｜>", "<tool>", "<tool><call>", "<x>"
+WORDS = ["a", "b", " ", "  ", "\n", "\n\n", "\t", "1", "12", "1234", "日本", "語", "🙂", ".", "'s", "def", " x",
+         "(", ")", "<", ">", "｜", "<｜", "Call", "call", "tool", "end"]
+
+
+def tokenizer(**mark) -> Tokenizer:
+    """A byte-level BPE like DeepSeek's, with a normalizer and added tokens; ``mark`` sets the flags of ``MARK``."""
+
+    tok = Tokenizer(models.BPE())
+    tok.normalizer = normalizers.Lowercase()
+    tok.pre_tokenizer = pre_tokenizers.Sequence([pre_tokenizers.Split(Regex(r"\p{N}{1,3}"), "isolated"),
+                                                 pre_tokenizers.ByteLevel(add_prefix_space=False)])
+    trainer = trainers.BpeTrainer(vocab_size=300, initial_alphabet=pre_tokenizers.ByteLevel.alphabet(),
+                                  show_progress=False)
+    tok.train_from_iterator(["def call(x): return x  # 日本語 🙂 tool end 1234\n"] * 50, trainer)
+    tok.add_special_tokens([TURN, END])
+    tok.add_tokens([AddedToken(TOOL, normalized=False), AddedToken(CALL, normalized=False),
+                    AddedToken("call", normalized=True), AddedToken(MARK, normalized=False, **mark)])
+    return tok
+
+
+class Counting:
+    """The tokenizer, recording each text it is asked to encode."""
+
+    def __init__(self, tok):
+        self.tok, self.encoded = tok, []
+
+    def get_added_tokens_decoder(self):
+        return self.tok.get_added_tokens_decoder()
+
+    def encode_batch(self, texts, add_special_tokens=False):
+        self.encoded += texts
+        return self.tok.encode_batch(texts, add_special_tokens=add_special_tokens)
+
+
+def full(tok, text):
+    return tok.encode(text, add_special_tokens=False).ids
+
+
+def pieces_of(tok, **kwargs) -> PromptPieces:
+    pieces = PromptPieces.of(tok, **kwargs)
+    assert pieces is not None
+    return pieces
+
+
+@pytest.mark.parametrize("mark", [{}, {"lstrip": True}])
+def test_ids_equal_the_tokenizers_on_texts_with_added_tokens_anywhere(mark):
+    tok, rng = tokenizer(**mark), random.Random(0)
+    pieces = pieces_of(tok, budget=200)       # small: pieces are dropped and encoded again along the way
+    marks = [TURN, END, TOOL, CALL, MARK, " " + MARK, TOOL + "<call", TOOL + CALL]
+    texts = ["", TURN, END + END, " " + TURN + " ", "a" * 3000 + TURN + "b"]
+    texts += ["".join(rng.choice(marks) if rng.random() < 0.2 else rng.choice(WORDS)
+                      for _ in range(rng.randint(1, 50))) for _ in range(1500)]
+    for text in texts:
+        assert pieces.ids(text) == full(tok, text), text
+
+
+def test_a_resent_conversation_encodes_only_its_new_pieces():
+    tok = Counting(tokenizer())
+    pieces = pieces_of(tok)
+    turn1 = TURN + "def call(x):\n  return 12 * x\n" * 200 + END
+    turn2 = TURN + "and 日本語? 🙂" + END
+    assert pieces.ids(turn1) == full(tok.tok, turn1)
+    tok.encoded.clear()
+    assert pieces.ids(turn1 + turn2 + "tail") == full(tok.tok, turn1 + turn2 + "tail")
+    assert tok.encoded == ["and 日本語? 🙂" + END, "tail"]       # TURN alone is a piece seen before
+
+
+@pytest.mark.parametrize("mark", [{"rstrip": True}, {"single_word": True}])
+def test_a_tokenizer_whose_added_tokens_move_a_split_gets_no_pieces(mark):
+    assert PromptPieces.of(tokenizer(**mark)) is None
+
+
+def test_special_tokens_encoded_as_text_get_no_pieces():
+    tok = tokenizer()
+    tok.encode_special_tokens = True
+    assert PromptPieces.of(tok) is None
+
+
+def test_a_tokenizer_without_added_tokens_or_batches_gets_no_pieces():
+    assert PromptPieces.of(Tokenizer(models.BPE())) is None
+    assert PromptPieces.of(object()) is None
+
+
+def test_the_pieces_kept_stay_within_the_budget():
+    tok = tokenizer()
+    pieces = pieces_of(tok, budget=50)
+    for i in range(40):
+        text = f"{TURN}turn {i} " + "x" * i + END
+        assert pieces.ids(text) == full(tok, text)
+        assert pieces._held <= 50 and pieces._held == sum(len(ids) for ids in pieces._kept.values())
+
+
+def test_the_cuda_server_encodes_chat_prompts_through_its_pieces(tmp_path):
+    pytest.importorskip("jinja2")
+    from tensorfold.cuda.server import App
+
+    tokenizer().save(str(tmp_path / "tokenizer.json"))
+    template = "{% for m in messages %}" + TURN + "{{ m.content }}" + END + "{% endfor %}"
+    (tmp_path / "tokenizer_config.json").write_text(json.dumps({"chat_template": template}))
+    app = App(SimpleNamespace(eos=(0,)), tmp_path, "test")
+    messages = [{"role": "user", "content": "def call(x): return 12 * x"}]
+    for turn in range(3):
+        prompt = app.prepare({"messages": messages, "max_tokens": 1}, True).prompt
+        assert prompt == full(app.tok, app.template.render(messages, tools=None, enable_thinking=False))
+        messages += [{"role": "assistant", "content": f"answer {turn}"}, {"role": "user", "content": f"more {turn}"}]
+    pieces = app._prompt_pieces()
+    assert pieces is not None and "def call(x): return 12 * x" + END in pieces._kept