diff --git a/httpx/_client.py b/httpx/_client.py
index 3465a10b75..e9730c93a3 100644
--- a/httpx/_client.py
+++ b/httpx/_client.py
@@ -559,6 +559,7 @@ def __init__(
         verify: VerifyTypes = True,
         cert: CertTypes = None,
         http2: bool = False,
+        http2_prior_knowledge: bool = False,
         proxies: ProxiesTypes = None,
         mounts: typing.Mapping[str, httpcore.SyncHTTPTransport] = None,
         timeout: TimeoutTypes = DEFAULT_TIMEOUT_CONFIG,
@@ -583,6 +584,9 @@ def __init__(
             trust_env=trust_env,
         )
 
+        if http2_prior_knowledge:
+            http2 = True
+
         if http2:
             try:
                 import h2  # noqa
@@ -1192,6 +1196,7 @@ def __init__(
         verify: VerifyTypes = True,
         cert: CertTypes = None,
         http2: bool = False,
+        http2_prior_knowledge: bool = False,
         proxies: ProxiesTypes = None,
         mounts: typing.Mapping[str, httpcore.AsyncHTTPTransport] = None,
         timeout: TimeoutTypes = DEFAULT_TIMEOUT_CONFIG,
@@ -1216,6 +1221,9 @@ def __init__(
             trust_env=trust_env,
         )
 
+        if http2_prior_knowledge:
+            http2 = True
+
         if http2:
             try:
                 import h2  # noqa
@@ -1239,6 +1247,7 @@ def __init__(
             verify=verify,
             cert=cert,
             http2=http2,
+            http2_prior_knowledge=http2_prior_knowledge,
             limits=limits,
             transport=transport,
             app=app,
@@ -1255,6 +1264,7 @@ def __init__(
                 verify=verify,
                 cert=cert,
                 http2=http2,
+                http2_prior_knowledge=http2_prior_knowledge,
                 limits=limits,
                 trust_env=trust_env,
             )
@@ -1271,6 +1281,7 @@ def _init_transport(
         verify: VerifyTypes = True,
         cert: CertTypes = None,
         http2: bool = False,
+        http2_prior_knowledge: bool = False,
         limits: Limits = DEFAULT_LIMITS,
         transport: httpcore.AsyncHTTPTransport = None,
         app: typing.Callable = None,
@@ -1283,7 +1294,12 @@ def _init_transport(
             return ASGITransport(app=app)
 
         return AsyncHTTPTransport(
-            verify=verify, cert=cert, http2=http2, limits=limits, trust_env=trust_env
+            verify=verify,
+            cert=cert,
+            http2=http2,
+            http2_prior_knowledge=http2_prior_knowledge,
+            limits=limits,
+            trust_env=trust_env,
         )
 
     def _init_proxy_transport(
@@ -1292,6 +1308,7 @@ def _init_proxy_transport(
         verify: VerifyTypes = True,
         cert: CertTypes = None,
         http2: bool = False,
+        http2_prior_knowledge: bool = False,
         limits: Limits = DEFAULT_LIMITS,
         trust_env: bool = True,
     ) -> httpcore.AsyncHTTPTransport:
@@ -1299,6 +1316,7 @@ def _init_proxy_transport(
             verify=verify,
             cert=cert,
             http2=http2,
+            http2_prior_knowledge=http2_prior_knowledge,
             limits=limits,
             trust_env=trust_env,
             proxy=proxy,
diff --git a/httpx/_config.py b/httpx/_config.py
index 837519afb5..3175085f51 100644
--- a/httpx/_config.py
+++ b/httpx/_config.py
@@ -45,9 +45,14 @@ def create_ssl_context(
     verify: VerifyTypes = True,
     trust_env: bool = True,
     http2: bool = False,
+    http2_prior_knowledge: bool = False,
 ) -> ssl.SSLContext:
     return SSLConfig(
-        cert=cert, verify=verify, trust_env=trust_env, http2=http2
+        cert=cert,
+        verify=verify,
+        trust_env=trust_env,
+        http2=http2,
+        http2_prior_knowledge=http2_prior_knowledge,
     ).ssl_context
 
 
@@ -65,11 +70,13 @@ def __init__(
         verify: VerifyTypes = True,
         trust_env: bool = True,
         http2: bool = False,
+        http2_prior_knowledge: bool = False,
     ):
         self.cert = cert
         self.verify = verify
         self.trust_env = trust_env
         self.http2 = http2
+        self.http2_prior_knowledge = http2_prior_knowledge
         self.ssl_context = self.load_ssl_context()
 
     def load_ssl_context(self) -> ssl.SSLContext:
@@ -79,6 +86,7 @@ def load_ssl_context(self) -> ssl.SSLContext:
             f"cert={self.cert!r} "
             f"trust_env={self.trust_env!r} "
             f"http2={self.http2!r}"
+            f"http2_prior_knowledge={self.http2_prior_knowledge!r}"
         )
 
         if self.verify:
@@ -162,7 +170,12 @@ def _create_default_ssl_context(self) -> ssl.SSLContext:
         context.set_ciphers(DEFAULT_CIPHERS)
 
         if ssl.HAS_ALPN:
-            alpn_idents = ["http/1.1", "h2"] if self.http2 else ["http/1.1"]
+            if self.http2_prior_knowledge:
+                alpn_idents = ["h2"]
+            elif self.http2:
+                alpn_idents = ["http/1.1", "h2"]
+            else:
+                alpn_idents = ["http/1.1"]
             context.set_alpn_protocols(alpn_idents)
 
         if hasattr(context, "keylog_filename"):  # pragma: nocover (Available in 3.8+)
diff --git a/httpx/_transports/default.py b/httpx/_transports/default.py
index 84aeb26be8..2500c8a8a5 100644
--- a/httpx/_transports/default.py
+++ b/httpx/_transports/default.py
@@ -111,6 +111,7 @@ def __init__(
         verify: VerifyTypes = True,
         cert: CertTypes = None,
         http2: bool = False,
+        http2_prior_knowledge: bool = False,
         limits: Limits = DEFAULT_LIMITS,
         trust_env: bool = True,
         proxy: Proxy = None,
@@ -119,7 +120,13 @@ def __init__(
         retries: int = 0,
         backend: str = "auto",
     ) -> None:
-        ssl_context = create_ssl_context(verify=verify, cert=cert, trust_env=trust_env)
+        ssl_context = create_ssl_context(
+            verify=verify,
+            cert=cert,
+            trust_env=trust_env,
+            http2=http2,
+            http2_prior_knowledge=http2_prior_knowledge,
+        )
 
         if proxy is None:
             self._pool = httpcore.AsyncConnectionPool(
@@ -128,6 +135,7 @@ def __init__(
                 max_keepalive_connections=limits.max_keepalive_connections,
                 keepalive_expiry=limits.keepalive_expiry,
                 http2=http2,
+                http2_prior_knowledge=http2_prior_knowledge,
                 uds=uds,
                 local_address=local_address,
                 retries=retries,