diff --git a/ChangeLog b/ChangeLog
index b0a01c0..8d10ea2 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -18,6 +18,9 @@
      Fixes #1040.
    * Fix C89 incompatibility in benchmark.c. Contributed by Brendan Shanks.
      #1353
+   * Fix parsing of PKCS#8 encoded Elliptic Curve keys. Previously Mbed TLS was
+     unable to parse keys with only the optional parameters field of the
+     ECPrivateKey structure. Found by jethrogb, fixed in #1379.
 
 Changes
    * Support cmake build where Mbed TLS is a subproject. Fix
diff --git a/library/pkparse.c b/library/pkparse.c
index 106533a..26a8b70 100644
--- a/library/pkparse.c
+++ b/library/pkparse.c
@@ -861,7 +861,10 @@
             mbedtls_ecp_keypair_free( eck );
             return( MBEDTLS_ERR_PK_KEY_INVALID_FORMAT + ret );
         }
+    }
 
+    if( p != end )
+    {
         /*
          * Is 'publickey' present? If not, or if we can't read it (eg because it
          * is compressed), create it from the private key.
diff --git a/tests/data_files/Makefile b/tests/data_files/Makefile
index 05029ab..2a7a50c 100644
--- a/tests/data_files/Makefile
+++ b/tests/data_files/Makefile
@@ -620,7 +620,86 @@
 ### Generate all RSA keys
 keys_rsa_all: keys_rsa_unenc keys_rsa_enc_basic keys_rsa_enc_pkcs8_v1 keys_rsa_enc_pkcs8_v2
 
+################################################################
+#### Generate various EC keys
+################################################################
 
+###
+### PKCS8 encoded
+###
+
+ec_prv.pk8.der:
+	$(OPENSSL) genpkey -algorithm EC -pkeyopt ec_paramgen_curve:prime192v1 -pkeyopt ec_param_enc:named_curve -out $@ -outform DER
+all_final += ec_prv.pk8.der
+
+# ### Instructions for creating `ec_prv.pk8nopub.der`,
+# ### `ec_prv.pk8nopubparam.der`, and `ec_prv.pk8param.der` by hand from
+# ### `ec_prv.pk8.der`.
+#
+# These instructions assume you are familiar with ASN.1 DER encoding and can
+# use a hex editor to manipulate DER.
+#
+# The relevant ASN.1 definitions for a PKCS#8 encoded Elliptic Curve key are:
+#
+# PrivateKeyInfo ::= SEQUENCE {
+#   version                   Version,
+#   privateKeyAlgorithm       PrivateKeyAlgorithmIdentifier,
+#   privateKey                PrivateKey,
+#   attributes           [0]  IMPLICIT Attributes OPTIONAL
+# }
+#
+# AlgorithmIdentifier  ::=  SEQUENCE  {
+#   algorithm   OBJECT IDENTIFIER,
+#   parameters  ANY DEFINED BY algorithm OPTIONAL
+# }
+#
+# ECParameters ::= CHOICE {
+#   namedCurve         OBJECT IDENTIFIER
+#   -- implicitCurve   NULL
+#   -- specifiedCurve  SpecifiedECDomain
+# }
+#
+# ECPrivateKey ::= SEQUENCE {
+#   version        INTEGER { ecPrivkeyVer1(1) } (ecPrivkeyVer1),
+#   privateKey     OCTET STRING,
+#   parameters [0] ECParameters {{ NamedCurve }} OPTIONAL,
+#   publicKey  [1] BIT STRING OPTIONAL
+# }
+#
+# `ec_prv.pk8.der` as generatde above by OpenSSL should have the following
+# fields:
+#
+# * privateKeyAlgorithm       namedCurve
+# * privateKey.parameters     NOT PRESENT
+# * privateKey.publicKey      PRESENT
+# * attributes                NOT PRESENT
+#
+# # ec_prv.pk8nopub.der
+#
+# Take `ec_prv.pk8.der` and remove `privateKey.publicKey`.
+#
+# # ec_prv.pk8nopubparam.der
+#
+# Take `ec_prv.pk8nopub.der` and add `privateKey.parameters`, the same value as
+# `privateKeyAlgorithm.namedCurve`. Don't forget to add the explicit tag.
+#
+# # ec_prv.pk8param.der
+#
+# Take `ec_prv.pk8.der` and add `privateKey.parameters`, the same value as
+# `privateKeyAlgorithm.namedCurve`. Don't forget to add the explicit tag.
+
+ec_prv.pk8.pem: ec_prv.pk8.der
+	$(OPENSSL) pkey -in $< -inform DER -out $@
+all_final += ec_prv.pk8.pem
+ec_prv.pk8nopub.pem: ec_prv.pk8nopub.der
+	$(OPENSSL) pkey -in $< -inform DER -out $@
+all_final += ec_prv.pk8nopub.pem
+ec_prv.pk8nopubparam.pem: ec_prv.pk8nopubparam.der
+	$(OPENSSL) pkey -in $< -inform DER -out $@
+all_final += ec_prv.pk8nopubparam.pem
+ec_prv.pk8param.pem: ec_prv.pk8param.der
+	$(OPENSSL) pkey -in $< -inform DER -out $@
+all_final += ec_prv.pk8param.pem
 
 ################################################################
 ### Generate certificates for CRT write check tests
diff --git a/tests/data_files/ec_prv.noopt.der b/tests/data_files/ec_prv.pk8nopub.der
similarity index 100%
rename from tests/data_files/ec_prv.noopt.der
rename to tests/data_files/ec_prv.pk8nopub.der
Binary files differ
diff --git a/tests/data_files/ec_prv.pk8nopub.pem b/tests/data_files/ec_prv.pk8nopub.pem
new file mode 100644
index 0000000..0ec5272
--- /dev/null
+++ b/tests/data_files/ec_prv.pk8nopub.pem
@@ -0,0 +1,4 @@
+-----BEGIN PRIVATE KEY-----
+MEECAQAwEwYHKoZIzj0CAQYIKoZIzj0DAQcEJzAlAgEBBCDH78XUX+cxmTPQ1hVkYbu3VvBc9c82
+EyGKaGvkAo1Pkw==
+-----END PRIVATE KEY-----
diff --git a/tests/data_files/ec_prv.pk8nopubparam.der b/tests/data_files/ec_prv.pk8nopubparam.der
new file mode 100644
index 0000000..70d30fb
--- /dev/null
+++ b/tests/data_files/ec_prv.pk8nopubparam.der
Binary files differ
diff --git a/tests/data_files/ec_prv.pk8nopubparam.pem b/tests/data_files/ec_prv.pk8nopubparam.pem
new file mode 100644
index 0000000..5c910c9
--- /dev/null
+++ b/tests/data_files/ec_prv.pk8nopubparam.pem
@@ -0,0 +1,4 @@
+-----BEGIN PRIVATE KEY-----
+ME0CAQAwEwYHKoZIzj0CAQYIKoZIzj0DAQcEMzAxAgEBBCDH78XUX+cxmTPQ1hVkYbu3VvBc9c82
+EyGKaGvkAo1Pk6AKBggqhkjOPQMBBw==
+-----END PRIVATE KEY-----
diff --git a/tests/data_files/ec_prv.pk8param.der b/tests/data_files/ec_prv.pk8param.der
new file mode 100644
index 0000000..8bbaa3a
--- /dev/null
+++ b/tests/data_files/ec_prv.pk8param.der
Binary files differ
diff --git a/tests/data_files/ec_prv.pk8param.pem b/tests/data_files/ec_prv.pk8param.pem
new file mode 100644
index 0000000..978beca
--- /dev/null
+++ b/tests/data_files/ec_prv.pk8param.pem
@@ -0,0 +1,5 @@
+-----BEGIN PRIVATE KEY-----
+MIGTAgEAMBMGByqGSM49AgEGCCqGSM49AwEHBHkwdwIBAQQgx+/F1F/nMZkz0NYVZGG7t1bwXPXP
+NhMhimhr5AKNT5OgCgYIKoZIzj0DAQehRANCAARkJXH1LofHesYJwJkoZQ0ijCVrxDFEi8e/fc1d
+6DS2Hsk55TWpL953QEIDN8RmW01lejceK3jQWs0uGDenGCcM
+-----END PRIVATE KEY-----
diff --git a/tests/suites/test_suite_pkparse.data b/tests/suites/test_suite_pkparse.data
index 6963882..acd2cd9 100644
--- a/tests/suites/test_suite_pkparse.data
+++ b/tests/suites/test_suite_pkparse.data
@@ -982,10 +982,6 @@
 depends_on:MBEDTLS_PEM_PARSE_C:MBEDTLS_ECP_C:MBEDTLS_ECP_DP_SECP192R1_ENABLED
 pk_parse_keyfile_ec:"data_files/ec_prv.sec1.der":"NULL":0
 
-Parse EC Key #1a (SEC1 DER, no optional part)
-depends_on:POLARSSL_PEM_PARSE_C:POLARSSL_ECP_C:POLARSSL_ECP_DP_SECP256R1_ENABLED
-pk_parse_keyfile_ec:"data_files/ec_prv.noopt.der":"NULL":0
-
 Parse EC Key #2 (SEC1 PEM)
 depends_on:MBEDTLS_PEM_PARSE_C:MBEDTLS_ECP_C:MBEDTLS_ECP_DP_SECP192R1_ENABLED
 pk_parse_keyfile_ec:"data_files/ec_prv.sec1.pem":"NULL":0
@@ -998,10 +994,34 @@
 depends_on:MBEDTLS_ECP_C:MBEDTLS_ECP_DP_SECP192R1_ENABLED
 pk_parse_keyfile_ec:"data_files/ec_prv.pk8.der":"NULL":0
 
+Parse EC Key #4a (PKCS8 DER, no public key)
+depends_on:MBEDTLS_PEM_PARSE_C:MBEDTLS_ECP_C:MBEDTLS_ECP_DP_SECP256R1_ENABLED
+pk_parse_keyfile_ec:"data_files/ec_prv.pk8nopub.der":"NULL":0
+
+Parse EC Key #4b (PKCS8 DER, no public key, with parameters)
+depends_on:MBEDTLS_PEM_PARSE_C:MBEDTLS_ECP_C:MBEDTLS_ECP_DP_SECP256R1_ENABLED
+pk_parse_keyfile_ec:"data_files/ec_prv.pk8nopubparam.der":"NULL":0
+
+Parse EC Key #4c (PKCS8 DER, with parameters)
+depends_on:MBEDTLS_PEM_PARSE_C:MBEDTLS_ECP_C:MBEDTLS_ECP_DP_SECP256R1_ENABLED
+pk_parse_keyfile_ec:"data_files/ec_prv.pk8param.der":"NULL":0
+
 Parse EC Key #5 (PKCS8 PEM)
 depends_on:MBEDTLS_PEM_PARSE_C:MBEDTLS_ECP_C:MBEDTLS_ECP_DP_SECP192R1_ENABLED
 pk_parse_keyfile_ec:"data_files/ec_prv.pk8.pem":"NULL":0
 
+Parse EC Key #5a (PKCS8 PEM, no public key)
+depends_on:MBEDTLS_PEM_PARSE_C:MBEDTLS_ECP_C:MBEDTLS_ECP_DP_SECP256R1_ENABLED
+pk_parse_keyfile_ec:"data_files/ec_prv.pk8nopub.pem":"NULL":0
+
+Parse EC Key #5b (PKCS8 PEM, no public key, with parameters)
+depends_on:MBEDTLS_PEM_PARSE_C:MBEDTLS_ECP_C:MBEDTLS_ECP_DP_SECP256R1_ENABLED
+pk_parse_keyfile_ec:"data_files/ec_prv.pk8nopubparam.pem":"NULL":0
+
+Parse EC Key #5c (PKCS8 PEM, with parameters)
+depends_on:MBEDTLS_PEM_PARSE_C:MBEDTLS_ECP_C:MBEDTLS_ECP_DP_SECP256R1_ENABLED
+pk_parse_keyfile_ec:"data_files/ec_prv.pk8param.pem":"NULL":0
+
 Parse EC Key #6 (PKCS8 encrypted DER)
 depends_on:MBEDTLS_DES_C:MBEDTLS_SHA1_C:MBEDTLS_ECP_C:MBEDTLS_ECP_DP_SECP192R1_ENABLED
 pk_parse_keyfile_ec:"data_files/ec_prv.pk8.pw.der":"polar":0