diff --git a/llama_cpp/llama.py b/llama_cpp/llama.py
index 6836ea5..de06da0 100644
--- a/llama_cpp/llama.py
+++ b/llama_cpp/llama.py
@@ -5,7 +5,7 @@ import time
 import math
 import multiprocessing
 from typing import List, Optional, Union, Generator, Sequence, Iterator, Deque, Tuple
-from collections import deque
+from collections import deque, OrderedDict
 
 from . import llama_cpp
 from .llama_types import *
@@ -14,37 +14,50 @@ from .llama_types import *
 class LlamaCache:
     """Cache for a llama.cpp model."""
 
-    def __init__(self):
-        self.cache_state: Dict[Tuple[llama_cpp.llama_token, ...], "LlamaState"] = dict()
+    def __init__(self, capacity_bytes: int = (2 << 30)):
+        self.cache_state: OrderedDict[
+            Tuple[llama_cpp.llama_token, ...], "LlamaState"
+        ] = OrderedDict()
+        self.capacity_bytes = capacity_bytes
 
-    def _sorted_keys(self) -> List[Tuple[llama_cpp.llama_token, ...]]:
-        return [
-            key
-            for _, key in sorted(
-                ((len(key), key) for key in self.cache_state.keys()), reverse=True
-            )
-        ]
+    @property
+    def cache_size(self):
+        return sum([state.llama_state_size for state in self.cache_state.values()])
 
-    def _find_key(
-        self, key: Tuple[llama_cpp.llama_token, ...]
+    def _find_longest_prefix_key(
+        self,
+        key: Tuple[llama_cpp.llama_token, ...],
     ) -> Optional[Tuple[llama_cpp.llama_token, ...]]:
-        for k in self._sorted_keys():
-            if key[: len(k)] == k:
-                return k
-        return None
+        min_len = 0
+        min_key = None
+        keys = (
+            (k, Llama.longest_token_prefix(k, key)) for k in self.cache_state.keys()
+        )
+        for k, prefix_len in keys:
+            if prefix_len > min_len:
+                min_len = prefix_len
+                min_key = k
+        return min_key
 
     def __getitem__(self, key: Sequence[llama_cpp.llama_token]) -> "LlamaState":
-        _key = self._find_key(tuple(key))
+        key = tuple(key)
+        _key = self._find_longest_prefix_key(key)
         if _key is None:
-            raise KeyError(f"Key not found: {key}")
-        return self.cache_state[_key]
+            raise KeyError(f"Key not found")
+        value = self.cache_state[_key]
+        self.cache_state.move_to_end(_key)
+        return value
 
     def __contains__(self, key: Sequence[llama_cpp.llama_token]) -> bool:
-        return self._find_key(tuple(key)) is not None
+        return self._find_longest_prefix_key(tuple(key)) is not None
 
     def __setitem__(self, key: Sequence[llama_cpp.llama_token], value: "LlamaState"):
-        self.cache_state = dict()  # NOTE: Currently limit to one cache entry.
-        self.cache_state[tuple(key)] = value
+        key = tuple(key)
+        if key in self.cache_state:
+            del self.cache_state[key]
+        self.cache_state[key] = value
+        while self.cache_size > self.capacity_bytes:
+            self.cache_state.popitem(last=False)
 
 
 class LlamaState:
@@ -53,7 +66,7 @@ class LlamaState:
         eval_tokens: Deque[llama_cpp.llama_token],
         eval_logits: Deque[List[float]],
         llama_state,  # type: llama_cpp.Array[llama_cpp.c_uint8]
-        llama_state_size: llama_cpp.c_size_t,
+        llama_state_size: int,
     ):
         self.eval_tokens = eval_tokens
         self.eval_logits = eval_logits
@@ -526,10 +539,22 @@ class Llama:
                 "logprobs is not supported for models created with logits_all=False"
             )
 
-        if self.cache and prompt_tokens in self.cache:
-            if self.verbose:
-                print("Llama._create_completion: cache hit", file=sys.stderr)
-            self.load_state(self.cache[prompt_tokens])
+        if self.cache:
+            try:
+                cache_item = self.cache[prompt_tokens]
+                cache_prefix_len = Llama.longest_token_prefix(
+                    cache_item.eval_tokens, prompt_tokens
+                )
+                eval_prefix_len = Llama.longest_token_prefix(
+                    self.eval_tokens, prompt_tokens
+                )
+                if cache_prefix_len > eval_prefix_len:
+                    self.load_state(cache_item)
+                    if self.verbose:
+                        print("Llama._create_completion: cache hit", file=sys.stderr)
+            except KeyError:
+                if self.verbose:
+                    print("Llama._create_completion: cache miss", file=sys.stderr)
 
         finish_reason = "length"
         multibyte_fix = 0
@@ -1004,3 +1029,15 @@ class Llama:
         exps = [math.exp(float(x)) for x in logits]
         sum_exps = sum(exps)
         return [math.log(x / sum_exps) for x in exps]
+
+    @staticmethod
+    def longest_token_prefix(
+        a: Sequence[llama_cpp.llama_token], b: Sequence[llama_cpp.llama_token]
+    ):
+        longest_prefix = 0
+        for _a, _b in zip(a, b):
+            if _a == _b:
+                longest_prefix += 1
+            else:
+                break
+        return longest_prefix